Vibrational States Of Molecules Research Articles

Ultrafast control of vibrational states of polar molecules with subcycle unipolar pulses

We investigate theoretically the nonresonant excitation of vibrational levels in polar molecules by unipolar radiation pulses of duration much shorter than the characteristic period of the molecule's vibration. We consider several profiles of the potential of the interaction of atoms in a diatomic molecule and derive analytically the probabilities of the molecule's transition to excited vibrational states when driven by subcycle unipolar pulses. It is shown that the excitation efficiency is governed by the electric pulse area so that unipolar half-cycle pulses turn out to be the most efficient ones. We introduce the characteristic scale of the electric pulse area, which serves as a measure of the pulse action on the vibrational states of the molecule. The results are generalized to the interaction of excited vibrational and rotational states and it is shown that the behavior of the vibrational levels' populations versus the electric pulse area as well as the introduced characteristic scale stays valid.

Differentiation of primary CNS lymphoma and glioblastoma using Raman spectroscopy and machine learning algorithms.

Objective and Methods: Timely discrimination between primary CNS lymphoma (PCNSL) and glioblastoma is crucial for diagnosis and therapy, but also determines the intraoperative surgical course. Advanced radiological methods allow for their distinction to a certain extent but ultimately, biopsies are still necessary for final diagnosis. As an upcoming method that enables tissue analysis by tracking changes in the vibrational state of molecules via inelastic scattered photons, we used Raman Spectroscopy (RS) as a label free method to examine specimens of both tumor entities intraoperatively, as well as postoperatively in formalin fixed paraffin embedded (FFPE) samples. Results: We applied and compared statistical performance of linear and nonlinear machine learning algorithms (Logistic Regression, Random Forest and XGBoost), and found that Random Forest classification distinguished the two tumor entities with a balanced accuracy of 82.4% in intraoperative tissue condition and with 94% using measurements of distinct tumor areas on FFPE tissue. Taking a deeper insight into the spectral properties of the tumor entities, we describe different tumor-specific Raman shifts of interest for classification. Conclusions: Due to our findings, we propose RS as an additional tool for fast and non-destructive tumor tissue discrimination, which may help to choose the proper treatment option. RS may further serve as a useful additional tool for neuropathological diagnostics with little requirements for tissue integrity.

Quantum ergodicity and energy flow in molecules

We review a theory for coupled many-nonlinear oscillator systems that describes quantum ergodicity and energy flow in molecules. The theory exploits the isomorphism between quantum energy flow in Fock space, that is, vibrational state space, and single-particle quantum transport in disordered solid-state systems. The quantum ergodicity transition in molecules is thereby analogous to the Anderson transition in disordered solids. The theory reviewed here, local random matrix theory (LRMT), describes the nature of the quantum ergodicity transition, statistical properties of vibrational eigenstates, and quantum energy flow through the vibrational states of molecules. Predictions of LRMT have been observed in computational studies of coupled nonlinear oscillator systems, which are summarized here. We also review applications of LRMT to molecular spectroscopy and chemical reaction rate theory, including adoption of LRMT in theories that predict rates of conformational change of molecules taking place at energies corresponding to those below and above the quantum ergodicity transition. A number of specific examples are reviewed, including the application of LRMT to predict (1) dilution factors of IR spectra of organic molecules, (2) rates of conformational change in chemical and photochemical reactions, (3) conformational dynamics of biological molecules in molecular beams, (4) rates of hydrogen bond breaking and rearrangement in clusters of biological molecules and water, and (5) excited state proton transfer reactions in proteins.

Collision of atoms under action of external magnetic and laser radiation fields with formation of Fano-Feshbach resonances

We investigate collision of two atoms in an external magnetic field and in the field of laser radiation with formation of Fano-Feshbach resonances. At one-photon resonance of laser radiation with two discrete vibrational states of molecule the dressed states are formed (Autler-Townes effect) which form Fano-Feshbach resonances in interaction with the external magnetic field. In addition, the lower molecular vibrational state is coupled with the continuum of the elastic channel via also LICS (laser-induced continuum structure) forming laser-induced resonance. We obtain cross-sections of elastic and inelastic resonant scattering and expression for the scattering length depending on the external magnetic and laser radiation fields.

Local modes in vibration–rotation spectroscopy

AbstractThe present paper is concerned with the description of highly excited rotational and/or vibrational states of molecules in terms of localized vibrations or local modes. Local mode effects are most common in molecules with multiple equivalent H–X bonds, which give rise to equivalent H–X local mode stretching vibrations, and the theory is outlined for the simplest such case, that of an H2X molecule. In the local mode picture of molecular vibration, experimentally observed, initially unexpected near‐degeneracies of vibrational states at high vibrational excitation, and of rotation–vibration states at high rotational excitation, can be explained in a relatively straightforward manner. The local mode theory predicts relations between the conventional rotation–vibration parameters whose values are determined in least‐squares fittings to observed rotation–vibration transition frequencies or wavenumbers. It should be emphasized, however, that such relations are valid only for particular forms of the effective rotation–vibration Hamiltonian used in the spectral analysis. We illustrate the theory with examples of experimental spectroscopic work where local mode effects play an important role in the interpretation of the experimental findings. The fact that local mode vibrations not only cause clustering of highly excited vibrational energy levels, but also of highly rotationally excited rotation–vibration energy levels, has been understood fairly recently. We outline the theoretical background for this phenomenon and relate it to the existing experimental work. © 2012 John Wiley & Sons, Ltd.This article is categorized under: Theoretical and Physical Chemistry > Spectroscopy

Analytical perturbations of wave functions and energy levels of vibrational states of molecules

A method for investigating the excited vibrational states of molecules based on the analytical perturbation theory for linear operators is proposed. According to this theory, the similarity transformation of the total projector and the construction of the transforming function allow obtaining analytical representations of eigenvectors, and in the course of reduction, eigenvalues of the perturbed operator. Theoretical statements and formulas of contributions of analytical perturbations are applied to the investigation of vibrational-rotational interactions, determination of wave functions, and corresponding energy values of excited vibrational states of molecules.

The changes of macroscopic features and microscopic structures of water under influence of magnetic field

Influences of magnetic field on microscopic structures and macroscopic properties of water are studied by the spectrum techniques of infrared, Raman, visible, ultraviolet lights and X-ray. From these investigations, we know that the magnetic fields change the distribution of molecules and electrons, cause displacements and polarization of molecules and atoms, result in changes of dipole-moment transition and vibrational states of molecules and variation of transition probability of electrons, but does not alter the constitution of molecules and atoms. These are helpful in seeking the mechanism of magnetization of water. Meanwhile, we also measure the changed rules of the surface tension force, soaking effect or angle of contact, viscosity, rheology features, refraction index, dielectric constant and electric conductivity of magnetized water relative to that of pure water. The results show that the magnetic fields increase the soaking degree and hydrophobicity of water to materials, depress its surface-tension force, diminish the viscosity of war, enhance the feature of plastic flowing of water, and increase the refraction index, dielectric constant and electric conductivity of water after magnetization. These changes are caused by the above changes of microscopic structures under the action of magnetic field. Therefore, our studies are significant in science and has practical value of applications.

Rovibrational wave-packet manipulation using shaped midinfrared femtosecond pulses

We have calculated the propagation of rovibrational wave-packet in the $^{1}\ensuremath{\Sigma}$ state of $\mathrm{CO}$ and the $^{2}\ensuremath{\Pi}$ state of $\mathrm{NO}$ manipulated by shaped midinfrared femtosecond laser pulses. The rotational states of the molecules were fully taken into account in the calculation and the effects of the rotational states in the vibrational wave-packet evolution were examined in detail. As a result, it is found that rotational excitations associated with the vibrational excitation affect the wave-packet propagation drastically, which suggests that the rotational states should not be ignored when vibrational states of molecules are used as the target state for coherent control and qubits for quantum computation. For the experimental detection of the amplitude and phase information on the rovibrational wave-packets, the time profiles of the transition intensities from the rovibrational wave-packet to an electronically excited state were calculated. It is shown that both ionization and laser induced fluorescence signals contain information necessary for the analysis of the phase and relative amplitude of the rovibrational wave-packets.

A cartoon in one dimension of the hydrogen molecular ion

To illustrate the basic methodology involved in the quantum mechanics of molecules, a one-dimensional caricature of the hydrogen molecular ion (H+2) is presented, which is exactly solvable, in the Born–Oppenheimer approximation, in terms of elementary functions. The purpose of the exercise is to elucidate in a simple setting the standard approach to the electronic and vibrational states of molecules, a subject of interest to students of physics, chemistry and biology.

Effects of Temperature Variations with Height on the Nonequilibrium Populations of Vibrational States of Molecules in Planetary Atmospheres

The model of the standard problem of radiative transfer in a vibrational–rotational band that we suggested previously (Shved and Semenov, 2001) for a nonlocal thermodynamic equilibrium (non-LTE) in vibrational molecular states is used to study the populations of these states in a nonisothermal planetary atmosphere. The temperature profile in the atmosphere is specified as a temperature perturbation in the form of a Gaussian function that is superimposed on an isothermal atmosphere. We show that the temperature profile has a complex effect on the state populations, which makes it difficult to analytically represent this effect. We investigate the influence of the peculiar features of the temperature profile in an LTE layer on the non-LTE height and suggest a criterion for determining those features that weakly affect this height. Using the populations of the CO2 0110 and 0001 states in the atmospheres of the Earth and Mars as examples, we show that the formulas suggested for estimating the non-LTE height are efficient.

Nonstationary self-focusing of sound beams in a vibrationally excited molecular gas

Mechanisms of the self-action of sound in quasi-stationary gases with nonequilibrium-excited vibrational states of molecules are considered. It is demonstrated that the observation of a self-focusing of sound is possible in such media. Two mechanisms of the self-action of sound are responsible for the self-focusing in an acoustically active medium: the cooling of gas by sound and the excitation of acoustic streamings in opposite directions.

How to Have Your Cake and Eat It Too

Scanning probe microscopies are now well-established methods for making images of molecules and materials at the atomic level. But now, scanning probe methods can also measure spectroscopic properties--the energy levels of molecules. In his Research Commentary, Pethica discusses results presented in the same issue by Stipe et al. in which a scanned probe was used to study vibrational states of molecules on surfaces. As a demonstration of the technique, the researchers were able to detect the energy shift of a deuterated form of acetylene. The combination of spatial and spectroscopic resolution should provide a powerful tool for surface scientists.

Rovibrational state distribution of deuterium molecules resulting from D-atom interaction with Ni(110)

Using the REMPI technique we have studied the internal state distribution of deuterium molecules produced by the interaction of atomic deuterium with chemisorbed deuterium on Ni(110) at 180 K. We observed molecules in vibrational states up to v = 3 with a mean vibrational energy of 220 meV. The mean rotational energies of the molecules in the vibrational states v = 0 to 3 are 185 meV, 133 meV, 75 meV and 37 meV, respectively. The overall mean rotational energy amounts to 150 meV, again far in excess of the mean rotational energy of molecules accommodated to the surface. The data are consistent with direct interactions of the impinging particles with the adsorbed particles (Eley-Rideal reaction and collision induced desorption), for which it is assumed that a considerable amount of the potential and kinetic energy of the impinging atoms is channeled into translational and internal energy of the reaction products.

Nuclear fusion in excited hydrogen molecules

We evaluate the nuclear fusion rates in the excited vibrational states of molecules of hydrogen isotopes. The ground state fusion rate is increased by about eight orders of magnitude but even in the most favorable situation it is out of any possible experimental test. We discuss the effects due to the nuclear potential in different hyperfine states, and the improvements attainable using coherent states and a solid phase.

Two-photon dissociation of sulfur dioxide at 248 and 308 nm

The photodissociation of SO 2 after two-photon excitation at 248 and 308 nm has been studied by means of photofragment translational spectroscopy (PTS). With 308 nm excitation, the time-of-flight distributions of the SO photofragments exhibit high kinetic-energy thresholds which are assigned to the formation of SO(X 3Σ −) +O ( 3P), SO(X 3Σ −) +O ( 1D), and SO(a 1Δ) +O ( 3P). A weak vibrational structure indicates the production of SO(a 1Δ) molecules in vibrational states up to at least ν=8. After excitation at 248 nm, nine different primary processes are clearly identified leading to SO+O as well as to S+O 2 fragments in various electronic states. All observed kinetic energy thresholds conform to a dissociation energy D o=543 kJ/mol (45400 cm −1) for the reaction SO 2→SO+O and D o= 569 kJ/mol (47600 cm −1) for the reaction SO 2→S+O 2. Evidence was found for the formation of higher SO electronic states in the energy region 28000–31000 cm −1, in particular for the previously not observed SO (A″ 3Σ +) state which possesses a term energy T o close to 30000 cm −1. Furthermore, the PTS method, in providing a direct way to determine the electronic states of each individual fragment of a fragment pair, revealed that the spin is not conserved in the SO 2→SO+O dissociation.

The subduction of vibrational states of molecules from the momentum space of simple harmonic motion

A single-particle model of molecular vibrational states is proposed in which the normal modes are projected out of the body vibrations of an infinite simple harmonic sphere. This model assigns the spurious change of mass or centre of mass and leads to removal of mass monopoles and dipoles from the system. These conservation conditions impose strict boundary conditions on the potential and basis functions. On incorporation into the model they result in a set of loop equations in which the potential is proportional to the fundamental vibration. The simplest solutions to these equations strongly resemble the Poschl-Teller generalization of the Morse potential. The solutions have been extended to incorporate the repulsive states and generate the set of net attractive states appropriate to the anharmonic potential.

The intensity of scattering of fast electrons with change in the vibrational states of molecules

A general expression has been obtained for the form of the line of the energy loss spectrum of fast electrons as a result of scattering on a molecule for which the movement of the nuclei is examined in the harmonic approximation. The intensity, obtained from this expressiDn, of the stream of scattered electrons reaching the analyzer when a cutoff voltage is used has been represented in the form of the sum of the contributions from all the allowed scattering channels. A criterion has been given, for which the relationships for the intensity become the approximate expressions usually employed in the interpretation of experimental data. Present-day electron diffraction technique, based on the use of a cutoff potential, makes it possible to increase considerably the volume of information that can be extracted from experiments on the scattering of fast electrons [1, 2]. Thus the separate measurement of the total and elastic scattering makes it possible to estimate not only such molecular constants as the internuclear distances and the mean-square amplitudes of the vibrations, but also various quantities characterizing the electronic structure of molecules [3]. By using the cutoff potential to alter the number of allowed inelastic scattering channels, it is possible to obtain additional information on the vibrational states of a molecule. The present paper gives equations for calculating the intensity of the inelastic scattering of electrons, as a result of which there is a change in the vibrational states of the "target" molecule without change in the electronic state. A general expression has been obtained for the intensity of the stream of scattered electrons reaching the analyzer when a cutoff potential is used. The equations have been derived within the framework of the approximations traditionally employed in the theoretical description of electron diffraction experiments: the kinematic approximation for the scattering, the Born-Oppenheimer approximation for the separation of the motion of the electrons and the nuclei, and the harmonic approximation for the description of the motion of the nuclei. The probability of the conversion of a molecule from the state k to the state k' as a result of collision with fast electrons is given in these approximations by the relationship

Multiphoton excitation processes between vibrational states of molecules

An approximation method has been developed to evaluate the perturbation theory expressions for the probabilities of two- and three-photon transitions among vibrational-rotational levels of diatomic and polyatomic molecules. The sum over intermediate rotational states and the degenerate quantum number M is evaluated for a general case, and the sum over intermediate vibrational states for particular cases. The molecule is taken to be a rotating anharmonic oscillator. The electrical anharmonicity and the effects of the electronic states of the molecule are considered. Two- and three-photon processes, with or without the presence of near-resonant intermediate states, should be observable with available infrared lasers. However, the intensities predicted for the observation of three-photon excitation would result in more dominant effects such as dissociation or gas breakdown.

Role of collective behaviour in polyatomic molecules

In this paper arguments are advanced advocating the introduction of a continuum collective coordinate representation of the highly excited anharmonic vibrational states of molecules. The structure of the vibrational spectrum is considered and an illustrative example is examined; the example is that of a simple unimolecular rearrangement reaction.

Nonequilibrium dissociation of a molecular gas under the action of infrared resonance laser radiation

A theoretical analysis is made of the nonequilibrium dissociation of molecules under the action of laser radiation whose frequency coincides with the frequency of one of the vibrational modes of a molecule. Equations are obtained for the relationship between the dissociation rate constant and the vibrational temperature, on the one hand, and the laser radiation flux density, on the other. It is assumed that the characteristics of the molecules and the gas temperature are known. The vibrational states of molecules are considered in the harmonic oscillator approximation and also making allowance for the anharmonicity.