Anharmonic Constants Research Articles

Calculation of Spectroscopic Parameters of Diatomic Molecules with an Open Electron Shell

The spectroscopic parameters of the BeH and CH molecules with an open electron shell are calculated in the basis of the Slater functions. An analytical expression for the total electron energy of molecules with an open electron shell is obtained. The total electron energy of the BeH and CH molecules was calculated by the Hartree–Fock–Roothaan (HFR) method for seven internuclear distances, including the equilibrium internuclear distance. A table of total energy values is constructed depending on the internuclear distance R. The total energy of a diatomic molecule is approximated as a third-degree polynomial in R. Applying the least squares method to energy values from the above-mentioned table, an analytical formula for the total energy of the BeH and CH molecules is obtained as a function of R. The analytical formula for E(R) has allowed the spectroscopic parameters ωe (harmonic vibrational frequency), ωexe (anharmonicity constant), Be (rotational constant), and αe (rovibrational interaction constant) to be calculated.

Production of ultracold 85Rb133Cs molecules in the lowest ground state via the B1Π1 short-range state.

We investigate the production of cold 85Rb133Cs molecules in the lowest vibronic level of the ground electronic state via the B1Π1 short-range state. The photoassociation (PA) spectra of the B1Π1 state, including newly observed transition to 2 vibronic levels, are obtained by high sensitivity time-of-flight mass spectrometry. Based on these PA spectra, the harmonic and anharmonic constants of vibronic states are obtained, resulting in predicted vibronic energies with an uncertainty of 1-2 cm-1. The B1Π1 (v = 3) state is found to have the maximum production rate for ground-state molecules with a value of 3(1) × 104 s-1, which is 3 times larger than the value via the previously studied 23Π0+ (v = 10, J = 0) state with two-photon cascade decay. The populations of J = 0, 1, and 2 rotational levels of X1Σ+ (v = 0) state molecules formed via the B1Π1 (v = 3, J = 1) state are measured to be around 20%, 40%, and 20%. To quantify the coupling strength between the B1Π1 (v = 3) state and X1Σ+ (v = 0) state, the transition dipole moment between them is measured to be 7.2(2) × 10-3ea0, which is also 3 times larger than the value between the 23Π0+ (v=10) state and X1Σ+ (v = 0) state, meaning the B1Π1 (v = 3) state has a stronger coupling with the X1Σ+ (v = 0) state. Our detailed measurements provide relevant parameters for investigation on direct stimulated Raman adiabatic passage transfer between the atomic scattering state and molecular bound state for 85Rb133Cs molecules.

A New Approach to the Potential Energy of Solids

A general theory is developed to investigate the expression for potential energy without using (i) empirical results and (ii) process of parameterizing. The simple approach of thermodynamics is adopted to obtain the expressions for the interaction energy of solids in terms of interatomic separation and crystal volume. The new findings have been applied to obtain the expressions for bulk modulus and pressure. The variation of the potential energy function, which provides a means to understand the stability of a crystal has been found in excellent agreements to the earlier results. The use of obtained harmonic and anharmonic force constants may be of much help to understand the dynamical behavior of solids with special reference to the many-body theories.

A scattering rate model for accelerated evaluation of lattice thermal conductivity bypassing anharmonic force constants

Predicting the lattice thermal conductivity from the atomic structure is important to many scientific and engineering applications. However, the state-of-the-art method based on first-principles calculations of the three-phonon scattering process is bound with high computational cost, while semiempirical models such as the Slack equation are less accurate. In this work, we examined the theoretical background of the commonly used computational models for thermal conductivity evaluation and proposed an improved quasiharmonic model based on an early approximation for three-phonon scattering strength. This model has significantly reduced computational cost as compared to the full anharmonic lattice dynamics calculations but retains a fairly good quantitative accuracy comparing to many semiempirical models. It also allows one to include normal processes in phonon-phonon scattering and obtain the phonon relaxation times.

A2Πu and 14Σu- States of Br2+ Studied by [1+1] Two-Photon Dissociation Spectroscopy in a Cold Ion Beam.

The A2Πu-X2Πg and 14Σu--X2Πg electronic transition spectra of Br2+ have been studied in the 500-720 nm wavelength range in a cold ion beam using a cryogenic cylindrical ion trap velocity map imaging spectrometer. The cryogenic ion trap produces a rotationally and vibrationally cold mass selected ion beam of Br2+, which simplifies the experimental spectra from vibrational hot bands and bands of mixed isotopic species. Vibrationally resolved photofragment excitation spectra are recorded for individual isotopologues of Br2+ (79Br2+, 79Br81Br+, 81Br2+) by [1+1] two-photon dissociation spectroscopy. Velocity map imaging of the photofragmented Br+ ions provides complementary information in the determination of spin-orbit states involved in corresponding electronic transitions. An experimental identification of the 14Σu- state has becomes possible based on the present experimental results and previously reported theoretical calculations. Vibrational analyses of the photofragment excitation spectra have yielded spectroscopic parameters, including state origins, harmonic frequencies, and anharmonic constants, for both A2Πu and 14Σu- states. The observed A2Πu state spin-orbit splitting and the "spin-forbidden" 14Σu--X2Πg transition band intensities indicate considerable spin-orbit couplings between the 14Σu- and A2Πu states. In addition, two groups of weak vibrational bands are also observed in the experimental spectra of 79Br81Br+, which may be due to symmetry-forbidden transitions from the X2Πg ground state to low-lying gerade states.

Laser-induced fluorescence spectroscopy of jet-cooled WO in 18, 900–23, 500 cm−1

The laser-induced fluorescence (LIF) excitation spectra of WO molecule have been recorded in the energy range of 18,900–23,500 cm−1 using laser ablation of tungsten target and reaction with free jet expansion of oxygen. Totally 63 vibronic transition bands were observed, and 60 bands were grouped into 10 electronic transition progressions, where 8 electronic transition progressions have the X0+ state as the lower state, as well as 2 progressions have the X1 state as the lower state. The electronic transition systems [21.5]0+–X0+ and [23.3]1–X0+ were newly identified by LIF spectroscopy. The molecular constants, including rotational constant, vibrational frequency, vibrational anharmonic constant, in the electronic excited states were obtained through rotational analysis of the spectra. In addition, the fluorescence lifetimes of the vibronic states were measured under the collision-free condition by exponentially fitting the fluorescence decay.

First-principles calculation study on phonon thermal conductivity of thorium and plutonium dioxides: Intrinsic anharmonic phonon-phonon and extrinsic grain-boundary–phonon scattering effects

In nuclear engineering, thermal conductivity of nuclear fuel materials is one of the most essential thermophysical data in analyzing nuclear reactor safety and fuel performance. In order to establish a reliable technique of computation of their thermal conductivity, we apply a scheme based on first-principles electronic calculations and calculate phonon thermal conductivity of both plutonium and thorium dioxides in the range of room to operating temperature, 300–1700 K. In the employed scheme, all phonon properties, such as frequency, velocity, and relaxation time, are calculated from harmonic and third-order anharmonic force constants obtained through first-principles calculations. Using these phonon properties, phonon thermal conductivity and its temperature dependence are computed with a standard phonon transport theory. The calculation results show a quite good agreement with experiments for thorium dioxide in the above temperature range. As for plutonium dioxide, our results coincides with the latest experimental data, though there is a wide spread in literature data. Moreover, we evaluate grain-boundary effects on phonon thermal conduction and find that grain size larger than 5 μm hardly affects thermal conductivity within the temperature range considered. These results prove that the present first-principles scheme is reliably applicable to accurate computation of phonon thermal conductivity of fuel materials in the considered temperature range as long as the first-principles calculation reproduces their electronic structures and interatomic forces.

Anharmonicity of Vibrational Modes in Hydrogen Chloride-Water Mixtures.

A thorough analysis of molecular vibrations in the binary system hydrogen chloride/water is presented considering a set of small mixed and pure clusters. In addition to the conventional normal-mode analysis based on the diagonalization of the Hessian, anharmonic frequencies were obtained from the perturbative VPT2 and PT2-VSCF method using hybrid density functional theory. For all normal modes, potential energy curves were modeled by displacing the atoms from the minimum geometry along the normal mode vectors. Three model potentials, a harmonic potential, a Morse potential, and a fourth order polynomial, were applied to fit these curves. From these data, it was possible not only to characterize distinct vibrations as mainly harmonic, anharmonic, or involving higher order terms but also to extract force constants, k, and anharmonicity constants, xe. By investigating all different types of intramolecular vibrations including covalent stretching or bending vibrations and intermolecular vibrations such as librations, we could demonstrate that while vibrational frequencies can be obtained applying scaling factors to harmonic results, useful anharmonicity constants cannot be predicted in such a way and the usage of more elaborate vibrational methods is necessary. For each particular type of molecular vibration, we could however determine a relationship between the wavenumber or wavenumber shift and the anharmonicity constant, which allows us to estimate mode dependent anharmonicity constants for larger clusters in the future.

Theoretical study of anharmonic force field and spectroscopic constants for 1-chlorophosphaethene, CH2PCl and CD2PCl

The anharmonic force field and spectroscopy constants for CH2PCl are determined using CCSD(T), VPT2, and density functional theory employing cc-pVQZ basis sets. The molecule structure, rotational spectroscopic constants, and vibrational wave numbers are compared with the available experimental data. Anharmonicity constants, vibration-rotation interaction constants and cubic force constants are predicted. Vibrational wave numbers and rotational constants for CD2PCl are also determined using the same levels. The isotopic shifts of vibrational wave numbers are remarkable by D atom substitution for 1-chlorophosphaethene.

Ab Initio Calculations of Phonon Spectra in BaF2 and PbF2 Crystals

The density functional theory is used to calculate vibrational spectra, suggest dependencies of total energies and frequencies on BaF2 and PbF2 crystal lattice constants, and obtain the density of two phonon states in PbF2 crystal weighted by thermal occupation numbers. Due to the order-of-magnitude difference between metal and fluorine masses, acoustic and optical branches are determined by metal and fluorine vibrations, respectively. Therefore, phonon spectra can be demonstrated in two Brillouin zones, namely fluorine lattice and sublattice, the number of optical branches being decreased twice. Based on the suggested dependencies of total energies in the crystal and squared frequencies on the lattice parameter, anharmonicity constants are identified. It is shown that with increasing temperature the frequency attenuates. For PbF2 crystal, anharmonicity constants are shown to be higher than for BaF2 crystal, and this fact is supported by the experiment. The model of the density of two phonon states in PbF2 crystal shows that the temperature broadening of Raman frequency is more substantial than that of the infrared active phonon frequency.

First vibrational investigations of N2O–H2O, N2O–(H2O)2, and (N2O)2–H2O complexes from the far to the near-infrared spectral region by neon matrix isolation and ab initio calculations

We present for the first time the investigation of water molecules complexed with dinitrogen monoxide, two abundant molecules in atmosphere, in solid neon using Fourier transform infrared (IR) spectroscopy. We identify at least three complexes from concentration effects, N2O-H2O, N2O-(H2O)2, and (N2O)2-H2O, by observation of new absorption bands close to the monomer fundamental modes from the far to the near IR region. We highlight the presence of isomers for the N2O-H2O complex with the help of theoretical calculations at second order Møller-Plesset (MP2) and coupled-cluster single double triple-F12a/aug-cc-pVTZ levels. The observed frequencies for the N2O-(H2O)2 and (N2O)2-H2O complexes are compared with MP2/aug-cc-pVTZ harmonic data. Anharmonic coupling constants have been derived from the observations of overtones and combination bands.

Phonon anharmonic frequency shift induced by four-phonon scattering calculated from first principles

Phonon energies at finite temperatures shift away from their harmonic values due to anharmonicity. In this paper, we have realized the rigorous calculation of phonon energy shifts of silicon by three- and four-phonon scattering from first principles. The anharmonic fourth-order force constants are calculated by considering up to the fifth nearest neighbors. The results agree reasonably well with available data from inelastic neutron scattering throughout the Brillouin zone. Surprisingly, the frequency shifts of optical phonon modes near the Γ point are sensitive to the cutoff radius of the fourth-order force constants, in contrast to the four-phonon scattering rates, which nearly saturate when considering the second nearest neighbors. We have also compared the results with ab initio molecular dynamics simulations and found that the higher order of anharmonicity is important for optical phonons. Our work provides critical insight into the anharmonic phonon frequency shift and will have a significant impact on the thermal and optical applications.

Direct Measurement of Anharmonic Decay Channels of a Coherent Phonon.

We report channel-resolved measurements of the anharmonic coupling of the coherent A_{1g} phonon in photoexcited bismuth to pairs of high wave vector acoustic phonons. The decay of a coherent phonon can be understood as a parametric resonance process whereby the atomic displacement periodically modulates the frequency of a broad continuum of modes. This coupling drives temporal oscillations in the phonon mean-square displacements at the A_{1g} frequency that are observed across the Brillouin zone by femtosecond x-ray diffuse scattering. We extract anharmonic coupling constants between the A_{1g} and several representative decay channels that are within an order of magnitude of density functional perturbation theory calculations.

Phonon anharmonicities in supported graphene

The paper presents temperature-dependent Raman studies of anharmonic phonon properties of graphene as-grown on copper, transferred to copper, SiO2/Si, and Al2O3, as well as nitrogen-doped graphene on SiO2/Si. Different G and 2D peak position and linewidth temperature dependencies were obtained in the temperature range of 20–294 K, upon which anharmonic constants for 3- and 4-phonon processes were determined. Values of anharmonic constants obtained from G peak shift for undoped graphene on dielectric substrates were quantitatively close to both experimental results for unsupported graphene and theoretical predictions reported in the literature, while the values for graphene as-grown on copper were almost two orders of magnitude greater. The results were analyzed in terms of substrate effect on phonon properties of graphene. The present study is useful for taking into account anharmonic phonon effects in graphene when designing graphene-based nanoelectronic devices.

Vibrational States and Nitrile Lifetimes of Cyanophenylalanine Isotopomers in Solution.

Nitrile lifetimes and the structure of the vibrational state space of four isotopomers of cyanophenylalanine in solution are calculated. While the frequency of the nitrile of the four isotopomers decreases in the order 12C14N, 12C15N, 13C14N, and 13C15N, the lifetime varies nonmonotonically with the change in frequency. The vibrational properties of the molecules that control the lifetime are examined. The specific resonances that contribute to the lifetime are tuned by isotopic substitution, and the magnitudes of the anharmonic constants involved in the coupling of vibrations that mediate the lifetime of the nitrile vary with CN mass. The nature of the modes coupled to the nitrile varies, as the frequency of the nitrile changes with isotopic substitution. For some CN frequencies the modes coupled to the CN are rather localized to the ring, while at other frequencies the modes coupled to the CN are more delocalized. Comparison of the calculated frequencies and lifetimes with recent experimental measurements on these molecules is discussed.

Spectral concentration of thermal conductivity in GaN—A first-principles study

We find using first-principles analysis of thermal conductivity (k) in isotopically pure Gallium nitride (GaN) that almost 60% of the heat is conducted by phonons in a very narrow frequency range of 5–7 THz (spanning only 9% of the frequencies in GaN). This spectral focusing of thermal conductivity is found to be due to a combination of two effects—a large increase in lifetimes of phonons through suppression of anharmonic scattering in the 5–7 THz frequency range coupled with a large phonon density of states at the same frequencies. Understanding of the effect is provided by solving the phonon Boltzmann transport equation in the single mode relaxation time approximation along with the use of harmonic and anharmonic force constants derived from density functional theory. The results can have important implications for engineering the thermal performance of devices based on GaN.

Theoretical investigation of the electronic properties of alkali atoms interacting with helium rare gas using a pseudopotential approach

In this work, electronic properties of alkali atoms interacting with helium rare gas (CsHe and RbHe) are studied through a full configuration interaction calculation, in cooperation with a pseudopotential approach and core polarization potential. The adiabatic potential energy curves for the ground state and numerous excited states of CsHe and RbHe systems are investigated. The corresponding spectroscopic constants such as equilibrium distance Re, well depth De, vibrational constant ωe, anharmonic constant, rotational constant Be, and transition energy Te as well as the vibrational levels of all electronic states are computed. Finally, permanent and transition dipole moment curves for the sigma states are determined and analyzed.

High-resolution infrared spectroscopy of the ν26 band of isoprene

The high-resolution infrared spectrum of isoprene (C5H8) has been observed in the region of the ν26 band near 992 cm−1 using a quantum cascade laser-based spectrometer. Five prominent Q-branch features were observed and have been assigned to the ν26 band, the ν17 band, and three hot bands of these fundamental transitions. Supporting calculations of the anharmonic transition frequencies and excited state rotational constants were performed at the MP2/cc-pVTZ level of theory and were used to help assign and fit the observed features. Approximate excited state rotational constants for the ν26 and ν17 bands have been obtained by fitting the contours of the observed Q-branch features.

Theoretical study of the phonon properties of pure and ion doped CeO2 nanoparticles

Using a microscopic model taking into account the spin-phonon interactions we have studied the phonon properties of pure and ion doped CeO2 nanoparticles (NPs). The phonon energy ω decreases whereas the damping γ increases with increasing temperature and decreasing particle size. Near the Curie temperature in the NPs there appears a kink in ω(T) and γ(T). The phonon properties are very sensitive especially to the anharmonic spin-phonon interaction. In dependence of the radius of the doping ions compared to the host ones ω could be reduced (Pr,Sm,Nd,La) or enhanced (Co,Y,Cu). The changes of the lattice parameters lead to changes of the exchange interaction and anharmonic spin-phonon interaction constants. The phonon damping is always enhanced by the doped NPs. It is shown that the changes in the phonon energy and damping of ion doped CeO2 NPs are due to combined effects of size, strain or defect effects.

Theoretical studies of anharmonic effect on the main reactions involving in NO2 in fuel burning

Using the transition state (TS) theory, the anharmonic and harmonic rate constant are calculated by means of Yao and Lin method for the main reactions related to nitrogen dioxide (NO2) in fuel combustion processes, respectively. A junction occurs between the anharmonic and harmonic rate constant for some bimolecular reactions, and the anharmonic rate constant is higher than the harmonic rate constant at low temperature, normally. The anharmonic effect of those reactions is significant and can’t be neglected at high temperature. Moreover, the modification of the existing reaction mechanisms referring to NO2 in fuel combustion processes is achieved through rate constant.