Harmonic Vibrational Modes Research Articles

Quantification of Crystal Chemistry of Fe‐Mg Carbonates by Raman Microspectroscopy and Near‐Infrared Remote Sensing

AbstractOn Earth, carbonate minerals are widely used as recorders of the geological environments in which they formed. Here, we present a method designed to retrieve the crystal chemistry of Fe‐Mg carbonate minerals using infrared remote sensing or Raman spectroscopy. We analyzed a suite of well‐characterized Fe‐Mg carbonate minerals for which Raman spectra were obtained in two different laboratories, and IR spectra were measured in reflectance and transmission from the visible range to 25‐μm. We built calibration lines for the dependence of fundamental and harmonic vibrational modes position to the Mg# (defined as Mg# = 100 × Mg/(Mg + Fe + Ca + Mn)). These calibrations should enable retrieval of Mg# based on spectroscopic observations with a typical accuracy of 10. We discuss the framework of applicability of these calibrations and apply them to a typical CRISM spectrum of carbonates from the Nilli Fossae region of Mars.

Cyanocyclopentadiene-Annulated Polycyclic Aromatic Radical Anions: Predicted Negative Ion Photoelectron Spectra and Singlet-Triplet Energies of Cyanoindene and Cyanofluorene Radical Anions.

Isomer-specific negative ion photoelectron spectra (NIPES) of cyanoindene (C9H7CN) and cyanofluorene (C14H9N), acquired through the computation of Franck-Condon (FC) factors that utilize harmonic vibrational frequencies and normal mode vectors derived from density functional theory (DFT) at the B3LYP/aug-cc-pVQZ and 6-311++G(2d,2p) basis sets, are reported. The adiabatic electron affinity (EA) values of the ground singlet (S0) and the lowest lying triplet (T1) states are used to predict site-specific S0-T1 energies (ΔEST). The vibrational spectra of the S0 and T1 states are typified by ring distortion and ring C-C stretching vibrational progressions. Among all the S0 isomers in C9H7CN, the 2-cyanoindene (2-C9H7CN) is found to be the most stable at an EA of 0.716 eV, with the least stable isomer being the 1-C9H7CN at an EA of 0.208 eV. In C14H9N, the most stable S0 isomer, 2-cyanofluorene (2-C14H9N), has an EA of 0.781 eV. The least stable S0 isomer in C14H9N is the 9-C14H9N, with an EA of 0.364 eV. The FC calculations are designed to mimic simulations that would be performed to aid in the analysis of experimental spectra obtained in NIPE spectroscopic techniques. The vibrational spectra, adiabatic EAs, and ΔEST values reported in this study are intended to act as a guide for future gas-phase ion spectroscopic experiments and astronomical searches, especially with regard to the hitherto largely unexplored C14H9N isomers.

Transfer learning of hyperparameters for fast construction of anisotropic GPR models: design and application to the machine-learned force field FFLUX.

The polarisable machine-learned force field FFLUX requires pre-trained anisotropic Gaussian process regression (GPR) models of atomic energies and multipole moments to propagate unbiased molecular dynamics simulations. The outcome of FFLUX simulations is highly dependent on the predictive accuracy of the underlying models whose training entails determining the optimal set of model hyperparameters. Unfortunately, traditional direct learning (DL) procedures do not scale well on this task, especially when the hyperparameter search is initiated from a (set of) random guess solution(s). Additionally, the complexity of the hyperparameter space (HS) increases with the number of geometrical input features, at least for anisotropic kernels, making the optimization of hyperparameters even more challenging. In this study, we propose a transfer learning (TL) protocol that accelerates the training process of anisotropic GPR models by facilitating access to promising regions of the HS. The protocol is based on a seeding-relaxation mechanism in which an excellent guess solution is identified by rapidly building one or several small source models over a subset of the target training set before readjusting the previous guess over the entire set. We demonstrate the performance of this protocol by building and assessing the performance of DL and TL models of atomic energies and charges in various conformations of benzene, ethanol, formic acid dimer and the drug fomepizole. Our experiments suggest that TL models can be built one order of magnitude faster while preserving the quality of their DL analogs. Most importantly, when deployed in FFLUX simulations, TL models compete with or even outperform their DL analogs when it comes to performing FFLUX geometry optimization and computing harmonic vibrational modes.

Predicted Negative Ion Photoelectron Spectra of 1-, 2-, and 9-Cyanoanthracene Radical Anions and Computed Thermochemical Values of the Three Cyanoanthracene Isomers.

In this work, the negative ion photoelectron spectra of 1-, 2-, and 9-cyanoanthracene (anthracenecarbonitrile, ACN) radical anions, obtained via the calculation of Franck-Condon (FC) factors based on a harmonic oscillator model, are reported. The FC calculations utilize harmonic vibrational frequencies and normal mode vectors derived from density functional theory using the B3LYP/6-311++G (2d,2p) basis set. The removal of an electron from the doublet anion allows for the computation of the negative ion photoelectron spectra that represents the neutral ground singlet state (So) and the lowest triplet state (T1) in each of the three ACN molecules. The respective adiabatic electron affinity (EA) values for the So state in 1-, 2-, and 9-ACN isomers are calculated to be 1.353, 1.360, and 1.423 eV. The calculated EA of the 9-cyanoanthracene singlet isomer is in close agreement with the previously reported experimental value of 1.27 ± 0.1 eV. Calculations show that the T1 states in 1-, 2-, and 9-ACN are located 1.656, 1.663, and 1.599 eV above the So state. The calculated T1 negative ion spectra exhibit intense vibrational origins and weak FC activity beyond the origins, indicating little change in geometry following electron detachment from the doublet anionic state. Upon deprotonation, the EA values of the radical isomers increase by ∼400-700 meV, resulting in neutral deprotonated radicals with EAs between 1.740 and 2.220 eV. The calculated site-specific gas-phase acidity values of ACN isomers indicate that ACN molecules are more acidic than benzonitrile.

Hydrogen bonding guest-water interactions in pinacolone, tert-butyl amine, and tert-butylmethyl ether: a theoretical study on energetics, structure, and topological +

In guest-host interactions, guest molecules used for hydrogen bonding potential of clathrate hydrate cages are involved as "promoters" for hydrogen or methane storage. Among the promoter molecules, there are pinacolone and tert-butylmethyl ether containing oxygen atom, and tert-butyl amine among those containing nitrogen atom. The dimer and trimer interactions of these molecules with the water clusters were investigated. The cooperativity effect, which is a measure of the hydrogen bonding of these oxygen and nitrogen-containing complexes, was calculated and these complexes were analyzed. Moreover, molecular electrostatic potential (MEP) analysis was performed to determine intermolecular interactions. Clusters of several molecules may seem like a non-significant state of matter; however, in systematic studies with small clusters, important results can be obtained. Therefore, it is very useful to work with clusters to understand the properties of the dense phase, and this study aimed to examine the properties of structures, energies, infrared vibration frequencies, and topological parameters, which develop as a result of the interaction of structures in different clusters with water molecules. The MP2 level was performed using aug-cc-pVDZ basis set calculations for this study. Tight converting criteria were used in the optimization step. Harmonic vibrational modes were calculated at the MP2/aug-cc-pVDZ level. Each minima obtained from the MP2 level was subjected to single-point energy calculations using CCSD(T) levels with the aug-cc-pVDZ basis set by the Gaussian16 package program suite. Thetopological analyseswere performed withnon-covalent interaction (NCI). MEP surface of the complex was also composed by Gaussian program using the optimized geometry at a MP2/aug-cc-pvdz level.

New Equivalent Circuit of a Cymbal Transducer Incorporating the Third Harmonic Mode of Vibration

A cymbal transducer is composed of a pair of metal caps and a piezoceramic disk. Cymbal transducers arranged in an array exhibit broadband characteristics. Although the finite element method has been widely used for analyzing the transducer and its array, an equivalent circuit that allows efficient analysis was recently developed. However, this previously reported circuit was based solely on the fundamental vibration mode of the transducer, and is thus unsuitable for analyzing the broadband characteristics of the cymbal array. Therefore, to overcome this limitation, a new broadband equivalent circuit for the cymbal transducer was devised in the present study. The new circuit was constructed by incorporating terms related to the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$3^{\text {rd}}$ </tex-math></inline-formula> harmonic vibration mode of the cap and corresponding radiation impedance into the existing equivalent circuit. The validity of this novel circuit was verified by comparing the analysis results with those obtained from the measurement of acoustic characteristics exhibited by a cymbal-transducer specimen. Compared with the previous circuit, the new equivalent circuit allows more accurate analysis and design of a cymbal transducer over a wider frequency range.

Valence shell photoelectron angular distributions and vibrationally resolved spectra of imidazole: A combined experimental-theoretical study.

Linearly polarized synchrotron radiation has been used to record polarization dependent valence shell photoelectron spectra of imidazole in the photon energy range 21-100eV. These have allowed the photoelectron angular distributions, as characterized by the anisotropy parameter β, and the electronic state intensity branching ratios to be determined. Complementing these experimental data, theoretical photoionization partial cross sections and β-parameters have been calculated for the outer valence shell orbitals. The assignment of the structure appearing in the experimental photoelectron spectra has been guided by vertical ionization energies and spectral intensities calculated by various theoretical methods that incorporate electron correlation and orbital relaxation. Strong orbital relaxation effects have been found for the 15a', nitrogen lone-pair orbital. The calculations also predict that configuration mixing leads to the formation of several low-lying satellite states. The vibrational structure associated with ionization out of a particular orbital has been simulated within the Franck-Condon model using harmonic vibrational modes. The adiabatic approximation appears to be valid for the X 2A″ state, with the β-parameter for this state being independent of the level of vibrational excitation. However, for all the other outer valence ionic states, a disparity occurs between the observed and the simulated vibrational structure, and the measured β-parameters are at variance with the behavior expected at the level of the Franck-Condon approximation. These inconsistencies suggest that the excited electronic states may be interacting vibronically such that the nuclear dynamics occur over coupled potential energy surfaces.

Vibronic interaction in trans-dichloroethene studied by vibration- and angle-resolved photoelectron spectroscopy using 19-90 eV photon energy.

Valence photoelectron spectra and photoelectron angular distributions of trans-dichloroethene have been measured with vibrational resolution at photon energies between 19 eV and 90 eV. Calculations of photoelectron anisotropy parameters, β, and harmonic vibrational modes help provide initial insight into the molecular structure. The photon energy range encompasses the expected position of the atomic Cl 3p Cooper minimum. A corresponding dip observed here in the anisotropy of certain photoelectron bands permits the identification and characterization of those molecular orbitals that retain a localized atomic Cl character. The adiabatic approximation holds for the X2Au state photoelectron band, but vibronic coupling was inferred within the A-B-C and the D-E states by noting various failures of the Franck-Condon model, including vibrationally dependent β-parameters. This is further explored using the linear vibronic coupling model with interaction parameters obtained from ab initio calculations. The A/B photoelectron band is appreciably affected by vibronic coupling, owing to the low-lying conical intersection of the A2Ag and B2Bu states. The C2Bg band is also affected, but to a lesser extent. The adiabatic minima of the D2Au and E2Ag states are almost degenerate, and the vibronic interaction between these states is considerable. The potential energy surface of the D2Au state is predicted to have a double-minimum shape with respect to the au deformations of the molecular structure. The irregular vibrational structure of the resulting single photoelectron band reflects the non-adiabatic nuclear dynamics occurring on the two coupled potential energy surfaces above the energy of their conical intersection.

Statistical mechanics of local force dipole responses in computer glasses.

Soft quasilocalized modes (QLMs) are universally featured by structural glasses quenched from a melt, and are involved in several glassy anomalies such as the low-temperature scaling of their thermal conductivity and specific heat, and sound attenuation at intermediate frequencies. In computer glasses, QLMs may assume the form of harmonic vibrational modes under a narrow set of circumstances; however, direct access to their full distribution over frequency is hindered by hybridizations of QLMs with other low-frequency modes (e.g., phonons). Previous studies to overcome this issue have demonstrated that the response of a glass to local force dipoles serves as a good proxy for its QLMs; we, therefore, study here the statistical-mechanical properties of these responses in computer glasses, over a large range of glass stabilities and in various spatial dimensions, with the goal of revealing properties of the yet-inaccessible full distribution of QLMs' frequencies. We find that as opposed to the spatial-dimension-independent universal distribution of QLMs' frequencies ω (and, consequently, also of their stiffness κ = ω2), the distribution of stiffnesses associated with responses to local force dipoles features a (weak) dependence on spatial dimension. We rationalize this dependence by introducing a lattice model that incorporates both the real-space profiles of QLMs-associated with dimension-dependent long-range elastic fields-and the universal statistical properties of their frequencies. Based on our findings, we propose a conjecture about the form of the full distribution of QLMs' frequencies and its protocol-dependence. Finally, we discuss possible connections of our findings to basic aspects of glass formation and deformation.

A Theoretical Study on the Excited States of the KCCH Radical

Based on the C2v symmetry, the low-lying electronic states of the KCCH radical was studied in the complete active pace self-consistent field (CASSCF) and multi-configurational second-order perturbation theory (CASPT2) methods. For the low-lying electronic states of KCCH, the calculated harmonic vibrational modes are in agreement with theoretical reports. Moreover, the electron transitions of KCCH, from X1Σ+ to 21Σ+, 11Π, 21Π, 11Σ-, 13Σ+, 13Π, 23Π and 13Σ-, are predicted at 5.43, 5.59, 7.87, 5.50, 5.15, 5.73, 5.53 and 6.82 eV, respectively. The CASSCF/CASPT2 potential energy curves (PECs) were calculated for K+-loss dissociation from the 13Σ+, 23Σ+,13Π ,21Σ, 11Π and 21Π states. Analyses of electron transition and dissociation curves show the ionic properties in the metal–ligand bond for KCCH. The dissociation energy of the KCCH (X1Σ+)→CCH-(11Σ)+K+(S0) is 4.423 eV at the CASSCF/CASPT2 level.

Multi-level description of the vibronic dynamics of open quantum systems.

A new approximate coherent state path integral approach, which enables accurate and efficient dynamical treatment of model Hamiltonians that incorporate excited electronic states of multiple chromophores that are coupled to discrete high frequency harmonic vibrational modes, is presented. The approach is based on the mapping Hamiltonian formalism for the electronic states together with semiclassical coherent state expressions for the forward and backward propagators describing the quantum bath modes. The density matrix dynamics is propagated in the full coherent state basis for the electronic mapping and discrete vibrational mode oscillators using ensembles of weighted trajectories. An effective scheme for projecting the ensemble onto selected vibronic basis states is presented enabling the evolution of the reduced system density matrix to be monitored as well as exploring the importance of selected vibronic relaxation pathways in the multichromophore system dynamics. The approach is demonstrated for simple model Hamiltonians, and we show how this coherent state density matrix propagation approach for high frequency discrete harmonic vibrational modes can be combined with partial linearized density matrix propagation to treat an additional continuum bath of low frequency environmental modes that could, in principle, include anharmonicity.

Hydration of l-glycylvaline and l-glycylvalylglycine zwitterions: Structural and vibrational studies using DFT method

Solvent effects on the structural and vibrational features of l-glycylvaline (L-GV) and l-glycylvalylglycine (L-GVG) in zwitterionic forms have been performed by means of DFT method. Relaxed potential energy surface scans (RPES) performed at B3LYP/6–31++G(d) level were used to map the reaction coordinate surfaces and to identify the geometries corresponding to the minima energy. Explicit solvation model, where L-GV and L-GVG are respectively surrounded by 9 and 11 water molecules interacting with H-donor and H-acceptor sites, as well as the different hybrid solvation models of solvation (explicit/COSMO, explicit/PCM and explicit/CPCM) allowed to analyze the hydration effects. Those number of water molecules are sufficient to fully hydrate carboxyl(CtOO-), amine (NtH3+) and amide (NH, C=O) groups. Harmonic vibrational modes calculated after geometry optimization on each solvated complex are performed at B3LYP/6–31++g(d) and PBE0/6–31++g(d) methods and a post-processing treatment enable us to assign the vibrational modes of LGV and L-GVG. The frequencies of the assigned modes obtained using B3LYP in explicit/COSMO are in good agreement with available IR and Raman values than those found in both explicit/PCM and explicit/CPCM which proved to be very close.

Universal Nonphononic Density of States in 2D, 3D, and 4D Glasses.

It is now well established that structural glasses possess disorder- and frustration-induced soft quasilocalized excitations, which play key roles in various glassy phenomena. Recent work has established that in model glass formers in three dimensions, these nonphononic soft excitations may assume the form of quasilocalized, harmonic vibrational modes whose frequency follows a universal density of states D(ω)∼ω^{4}, independently of microscopic details, and for a broad range of glass preparation protocols. Here, we further establish the universality of the nonphononic density of vibrational modes by direct measurements in model structural glasses in two dimensions and four dimensions. We also investigate their degree of localization, which is generally weaker in lower spatial dimensions, giving rise to a pronounced system-size dependence of the nonphononic density of states in two dimensions, but not in higher dimensions. Finally, we identify a fundamental glassy frequency scale ω_{c} above which the universal ω^{4} law breaks down.

Analysis of Harmonic Vibration Characteristics for a Composite Honeycomb Panel of the Spacecraft Scanner

The coordinate and frequency distributions of the values of displacement and acceleration amplitudes, the vibration acceleration amplification factors, and the equivalent von Mises stresses are obtained from the data on the simulation modeling of harmonic vibration of the composite honeycomb panel for spacecraft scanner and its related operational equipment (a scanner, magnetometer, optical devices, etc.) mounted on it. A dynamic simulation model of the composite honeycomb panel was developed using modern finite element analysis tools, such as ANSYS APDL. Carbon fiber reinforced plastic plates with an aluminum foil honeycomb core in the form of regularly shaped hexagonal cells that make up the honeycomb panel are approximated by multilayer plate finite elements. The related operational equipment, such as optical devices, a scanner and magnetometer, are represented in the model by lumped masses rigidly attached to the panel. The spectrum of natural frequencies and vibration modes of the spacecraft scanner honeycomb panel is determined using the developed simulation model. The resonant displacement and acceleration amplitudes, the vibration acceleration amplification factors as well as the distributions of the amplitudes of the equivalent von Mises stresses are obtained in the operating frequency range of the investigated harmonic vibration mode of the spacecraft scanner honeycomb panel.

Ab initio periodic modelling of the vibrational spectra of molecular crystals: the case of uracil

The structure and vibrational spectra of solid uracil have been simulated in the framework of Density Functional Theory (DFT) using a periodic unit cell model. Structural parameters are reproduced reasonably well by using the dispersion corrected, global hybrid Hartree–Fock/DFT functional B3LYP-D* and an all-electron, Gaussian type, triple zeta basis set with polarisation. The periodic calculation provides the full set of fundamental harmonic vibrational modes, whose nature can be investigated by inspecting the corresponding eigenvectors. Accounting for dispersive interactions indirectly affects the spectra, through the impact on the cell parameters. Marked differences are found between the gas and solid phase spectra, that can be related to either mode coupling or direct alteration of the potential energy via neighbour-neighbour molecular interactions. Anharmonicity needs to be considered for a meaningful comparison with experiments; a single scaling factor provides a significantly improved agreement for most of the frequencies, except for the NH stretchings, which require a larger downscaling. This rescaling strategy yields results of comparable quality with respect to previously reported calculations with a cluster model and a perturbative treatment of anharmonicity.

Commonalities in frequency-dependent viscoelastic damping in glasses in the MHz to THz regime

We use non-equilibrium molecular dynamics oscillatory shear simulations to study frequency-dependent viscoelastic damping spanning nearly six decades in frequency range (MHz to THz), in a wide range of model glasses including binary glasses such as Cu-Zr metallic glass (MG), Wahnström glass and amorphous silica, and unary glasses, namely, Dzugutov glass and amorphous silicon. First, for the Cu-Zr MG, we elucidate the role of quench rate, number of shear cycles, shear amplitude, and shear temperature on the damping characteristics. We observe striking commonalities in damping characteristics for all glasses studied—(i) a peak in the loss modulus in the high-frequency regime (∼THz) and (ii) persistent damping in the low-frequency regime (extending down to 10 s of MHz). The high-frequency peak is seen to overlap with the range of natural vibrational frequencies for each glass, and arises from coupling between the excited harmonic vibrational modes. On the other hand, persistent damping at intermediate and low frequencies is shown to be a result of long time-scale local, irreversible deformation.

On the structure of the simplest triselenide compound model and the stabilizing effect of water molecules

This study provides a molecular view of the simplest triselenide compound model, the hydrogen triselenide radical (HSe3) with Density Functional Theory (DFT), Møller–Plesset perturbation theory, and Coupled-Cluster theory. An analysis of the H–Se–Se–Se dihedral angle indicated barrier energies for the cis (1.8kcalmol−1) and trans (1.4kcalmol−1) configurations, which confirms the gauche conformation as the global minimum structure in the ground state with hydrogen atom out of plane. The central and the edge selenium–selenium bond lengths were predicted as 2.214–2.274 and 2.350–2.420Å, respectively, while an exploration of the edge Se–Se bond predicted a large polarized σ-bond revealing Wiberg (1.32) and Mayer order (1.31) bond order indices enhancing this feature. The influence of the population method on the prediction of the atomic charge distribution, the spin density, and the electric dipole moment was investigated. The harmonic and anharmonic vibrational frequency modes were also analyzed here. Moreover, the interaction between HSe3 and water molecules was investigated in order to explore the structural, electronic, and spectroscopic properties of monohydrated and dihydrated structures [HSe3(H2O)n; n=1,2]. Natural bond orbital (NBO) analysis and a topological analysis with the quantum theory of atoms in molecules (QTAIM) were employed to understand how the intermolecular interactions stabilize the triselenide compound.

Nonlinear modes disentangle glassy and Goldstone modes in structural glasses

One outstanding problem in the physics of glassy solids is understanding the statistics and properties of low-energy excitations that stem from the disorder that characterizes these systems' microstructure. In this work we introduce a family of algebraic equations whose solutions represent collective displacement directions (modes) in the multi-dimensional configuration space of a structural glass. We explain why solutions of the algebraic equations, coined nonlinear glassy modes, are quasi-localized low-energy excitations. We present an iterative method to solve the algebraic equations, and use it to study the energetic and structural properties of a selected subset of their solutions constructed by starting from a normal mode analysis of the potential energy of a model glass. Our key result is that the structure and energies associated with harmonic glassy vibrational modes and their nonlinear counterparts converge in the limit of very low frequencies. As nonlinear modes never suffer hybridizations, our result implies that the presented theoretical framework constitutes a robust alternative definition of `soft glassy modes' in the thermodynamic limit, in which Goldstone modes overwhelm and destroy the identity of low-frequency harmonic glassy modes.

Importance of Vibronic Effects in the UV-Vis Spectrum of the 7,7,8,8-Tetracyanoquinodimethane Anion.

We present a computational method for simulating vibronic absorption spectra in the ultraviolet-visible (UV-vis) range and apply it to the 7,7,8,8-tetracyanoquinodimethane anion (TCNQ-), which has been used as a ligand in black absorbers. Gaussian broadening of vertical electronic excitation energies of TCNQ- from linear-response time-dependent density functional theory produces only one band, which is qualitatively incorrect. Thus, the harmonic vibrational modes of the two lowest doublet states were computed, and the vibronic UV-vis spectrum was simulated using the displaced harmonic oscillator approximation, the frequency-shifted harmonic oscillator approximation, and the full Duschinsky formalism. An efficient real-time generating function method was implemented to avoid the exponential complexity of conventional Franck-Condon approaches to vibronic spectra. The obtained UV-vis spectra for TCNQ- agree well with experiment; the Duschinsky rotation is found to have only a minor effect on the spectrum. Born-Oppenheimer molecular dynamics simulations combined with calculations of the electronic excitation energies for a large number of molecular structures were also used for simulating the UV-vis spectrum. The Born-Oppenheimer molecular dynamics simulations yield a broadening of the energetically lowest peak in the absorption spectrum, but additional vibrational bands present in the experimental and simulated quantum harmonic oscillator spectra are not observed in the molecular dynamics simulations. Our results underline the importance of vibronic effects for the UV-vis spectrum of TCNQ-, and they establish an efficient method for obtaining vibronic spectra using a combination of linear-response time-dependent density functional theory and a real-time generating function approach.

Infrared and Ultraviolet Spectra of Diborane(6): B2H6 and B2D6.

We recorded absorption spectra of diborane(6), B2H6 and B2D6, dispersed in solid neon near 4 K in both mid-infrared and ultraviolet regions. For gaseous B2H6 from 105 to 300 nm, we report quantitative absolute cross sections; for solid B2H6 and for B2H6 dispersed in solid neon, we measured ultraviolet absorbance with relative intensities over a wide range. To assign the mid-infrared spectra to specific isotopic variants, we applied the abundance of (11)B and (10)B in natural proportions; we undertook quantum-chemical calculations of wavenumbers associated with anharmonic vibrational modes and the intensities of the harmonic vibrational modes. To aid an interpretation of the ultraviolet spectra, we calculated the energies of electronically excited singlet and triplet states and oscillator strengths for electronic transitions from the electronic ground state.