Vibrational Coordinates Research Articles

FTIR, FTRaman, UV–Visible and NMR spectroscopic studies on 3,3′,4,4′-tetrachloroazoxybenzene, an azoxybenzene derivative with toxic effects

We have synthesized 3,3′,4,4′ Tetrachloroazoxybenzene (TCAOB) and, later, characterized it by using infrared, Raman, 1H, 13C NMR and UV–visible spectroscopies. The structural, topological and vibrational properties of four Cis and three Trans isomers were theoretically predicted by using the hybrid B3LYP together with the 6-31G* and 6-311++G** basis sets. The 69 normal modes of vibration for all TCAOB isomers were assigned by using the scaled quantum mechanical force field (SQMFF) procedure and their experimental vibrational spectra and normal internal coordinates. The high stabilities of all Cis and Trans isomers are supported by the π→π*, n→σ*, n→π* and π*→π* electronic transitions calculated by NBO studies while the AIM analyses reveal for the Trans forms the existence of intra-molecular CH⋯O hydrogen bonds, as suggested by the broad IR band observed in the higher wavenumbers region. The low gap energy for the Trans I isomer supports their higher reactivity probably due to the repulsion of the more electronegative Cl and O atoms as a consequence of their proximities. In addition, the force constants for all Cis and Trans isomers were calculated by using both levels of theory. Here, the comparisons of the predicted IR, Raman, NMR and ultraviolet–visible spectra with the corresponding experimental ones demonstrate good concordances. The existence of the NO groups in all TCAOB isomers support the differences in their properties, as compared with those reported for TCAB.

Eckart ro-vibrational Hamiltonians via the gateway Hamilton operator: Theory and practice.

Recently, a general expression for Eckart-frame Hamilton operators has been obtained by the gateway Hamiltonian method [V. Szalay, J. Chem. Phys. 142, 174107 (2015) and V. Szalay, J. Chem. Phys. 143, 064104 (2015)]. The kinetic energy operator in this general Hamiltonian is nearly identical to that of the Eckart-Watson operator even when curvilinear vibrational coordinates are employed. Its different realizations correspond to different methods of calculating Eckart displacements. There are at least two different methods for calculating such displacements: rotation and projection. In this communication, the application of Eckart Hamiltonian operators constructed by rotation and projection, respectively, is numerically demonstrated in calculating vibrational energy levels. The numerical examples confirm that there is no need for rotation to construct an Eckart ro-vibrational Hamiltonian. The application of the gateway method is advantageous even when rotation is used since it obviates the need for differentiation of the matrix rotating into the Eckart frame. Simple geometrical arguments explain that there are infinitely many different methods for calculating Eckart displacements. The geometrical picture also suggests that a unique Eckart displacement vector may be defined as the shortest (mass-weighted) Eckart displacement vector among Eckart displacement vectors corresponding to configurations related by rotation. Its length, as shown analytically and demonstrated by numerical examples, is equal to or less than that of the Eckart displacement vector one can obtain by rotation to the Eckart frame.

Using monomer vibrational wavefunctions as contracted basis functions to compute rovibrational levels of an H2O-atom complex in full dimensionality.

In this paper, we present new ideas for computing rovibrational energy levels of molecules composed of two components and apply them to H2O-Cl-. When both components are themselves molecules, Euler angles that specify their orientation with respect to an axis system attached to the inter-monomer vector are used as vibrational coordinates. For H2O-Cl-, there is only one set of Euler angles. Using Euler angles as intermolecular vibrational coordinates is advantageous because in many cases coupling between them and coordinates that describe the shape of the monomers is unimportant. The monomers are not assumed to be rigid. In the most efficient calculation, vibrational wavefunctions of the monomers are used as contracted basis functions. Energy levels are calculated using the Lanczos algorithm.

High-Level ab Initio Predictions for the Ionization Energies, Bond Dissociation Energies, and Heats of Formation of Titanium Oxides and Their Cations (TiOn/TiOn+, n = 1 and 2).

The ionization energies (IEs) of TiO and TiO2 and the 0 K bond dissociation energies (D0) and the heats of formation at 0 K (ΔH°f0) and 298 K (ΔH°f298) for TiO/TiO+ and TiO2/TiO2+ are predicted by the wave-function-based CCSDTQ/CBS approach. The CCSDTQ/CBS calculations involve the approximation to the complete basis set (CBS) limit at the coupled cluster level up to full quadruple excitations along with the zero-point vibrational energy (ZPVE), high-order correlation (HOC), core-valence (CV) electronic, spin-orbit (SO) coupling, and scalar relativistic (SR) effect corrections. The present calculations yield IE(TiO) = 6.815 eV and are in good agreement with the experimental IE value of 6.819 80 ± 0.000 10 eV determined in a two-color laser-pulsed field ionization-photoelectron (PFI-PE) study. The CCSDT and MRCI+Q methods give the best predictions to the harmonic frequencies: ωe (ωe+) = 1013 (1069) and 1027 (1059) cm-1 and the bond lengths re (re+) = 1.625 (1.587) and 1.621 (1.588) Å, for TiO (TiO+) compared with the experimental values. Two nearly degenerate, stable structures are found for TiO2 cation: TiO2+(C2v) structure has two equivalent TiO bonds, while the TiO2+(Cs) structure features a long and a short TiO bond. The IEs for the TiO2+(C2v)←TiO2 and TiO2+(Cs)←TiO2 ionization transitions are calculated to be 9.515 and 9.525 eV, respectively, giving the theoretical adiabatic IE value in good agreement with the experiment IE(TiO2) = 9.573 55 ± 0.000 15 eV obtained in the previous vacuum ultraviolet (VUV)-PFI-PE study of TiO2. The potential energy surface of TiO2+ along the normal vibrational coordinates of asymmetric stretching mode (ω3+) is nearly flat and exhibits a double-well potential with the well of TiO2+ (Cs) situated around the central well of TiO2+(C2v). This makes the theoretical calculation of ω3+ infeasible. For the symmetric stretching (ω1+), the current theoretical predictions overestimate the experimental value of 829.1 ± 2.0 cm-1 by more than 100 cm-1. This work together with the previous experimental and theoretical investigations supports the conclusion that the CCSDTQ/CBS approach is capable of providing reliable IE and D0 predictions for TiO/TiO+ and TiO2/TiO2+ with error limits less than or equal to 60 meV. The CCSDTQ/CBS calculations give the predictions of D0(Ti+-O) - D0(Ti-O) = 0.004 eV and D0(O-TiO) - D0(O-TiO+) = 2.699 eV, which are also consistent with the respective experimental determination of 0.008 32 ± 0.000 10 and 2.753 75 ± 0.000 18 eV.

Revisiting the (E + A) ⊗ (e + a) problems of polyatomic systems with trigonal symmetry: general expansions of their vibronic Hamiltonians.

In this work, we derive general expansions in vibrational coordinates for the (E + A) ⊗ (e + a) vibronic Hamiltonians of molecules with one and only one C3 axis. We first derive the expansion for the lowest C3 symmetry. Additional symmetry elements systematically eliminate terms in the expansion. We compare our expansions with the previous results for two cases, the and the C3 (E + A) ⊗ e. The first comparison demonstrates the robustness, completeness, conciseness, and convenience of our formalism. There is a systematic discrepancy in the second comparison. We discuss the origin of the discrepancy and use a numerical example to corroborate our expansion. Our formalism covers 153 vibronic problems in 6 point groups. It also gives general expansions for the spin-orbit vibronic Hamiltonians of the p-type (E + A) ⊗ (e + a) problems.

Ab Initio Transient Vibrational Spectral Analysis

Pump probe spectroscopy techniques have enabled the direct observation of a variety of transient molecular species in both ground and excited electronic states. Time-resolved vibrational spectroscopy is becoming an indispensable tool for investigating photoinduced nuclear dynamics of chemical systems of all kinds. On the other hand, a complete picture of the chemical dynamics encoded in these spectra cannot be achieved without a full temporal description of the structural relaxation, including the explicit time-dependence of vibrational coordinates that are substantially displaced from equilibrium by electronic excitation. Here we present a transient vibrational analysis protocol combining ab initio direct molecular dynamics and time-integrated normal modes introduced in this work, relying on the recent development of analytic time-dependent density functional theory (TDDFT) second derivatives for excited states. Prototypical molecules will be used as test cases, showing the evolution of the vibrational signatures that follow electronic excitation. This protocol provides a direct route to assigning the vibrations implicated in the (photo)dynamics of several (photoactive) systems.

Effective representation of amide III, II, I, and A modes on local vibrational modes: Analysis of ab initio quantum calculation results

The Hamiltonian matrix for the first excited vibrational states of a protein can be effectively represented by local vibrational modes constituting amide III, II, I, and A modes to simulate various vibrational spectra. Methods for obtaining the Hamiltonian matrix from ab initio quantum calculation results are discussed, where the methods consist of three steps: selection of local vibrational mode coordinates, calculation of a reduced Hessian matrix, and extraction of the Hamiltonian matrix from the Hessian matrix. We introduce several methods for each step. The methods were assessed based on the density functional theory calculation results of 24 oligopeptides with four different peptide lengths and six different secondary structures. The completeness of a Hamiltonian matrix represented in the reduced local mode space is improved by adopting a specific atom group for each amide mode and reducing the effect of ignored local modes. The calculation results are also compared to previous models using C=O stretching vibration and transition dipole couplings. We found that local electric transition dipole moments of the amide modes are mainly bound on the local peptide planes. Their direction and magnitude are well conserved except amide A modes, which show large variation. Contrary to amide I modes, the vibrational coupling constants of amide III, II, and A modes obtained by analysis of a dipeptide are not transferable to oligopeptides with the same secondary conformation because coupling constants are affected by the surrounding atomic environment.

Ro-vibrational spectrum of H2O-Ne in the ν2 H2O bending region: A combined ab initio and experimental investigation

High resolution ro-vibrational transitions of the H2O-Ne complex in the ν2 bending region of H2O at 6μm have been measured using a rapid scan infrared spectrometer based on an external cavity quantum cascade laser and an astigmatic multipass optical cell. To aid the spectral assignment, a four-dimension potential energy surface of H2O-Ne which depends on the intramolecular bending coordinate of the H2O monomer and the three intermolecular vibrational coordinates has been constructed and the rovibrational transitions have been calculated. Three ortho and two para H2O-20Ne bands have been identified from the experimental spectra. Some weaker transitions belonging to H2O-22Ne have also been identified experimentally. Spectroscopic fits have been performed for both the experimental and theoretical transition frequencies using a simple pseudo-diatomic Hamiltonian including both Coriolis coupling and Fermi resonance terms. The experimental and theoretical spectroscopic constants thus obtained have been compared. Further improvements needed in the potential energy surface and the related spectral simulation have been discussed.

Diazomethane addition to sumanene as a subfullerene structure: A theoretical mechanistic study

In present study, kinetics and reaction mechanism of diazomethane and sumanene in gas phase were studied using quantum calculations at B3LYP/6-311+G(d,p) level of theory. Functionalization of the sumanene by this reaction was investigated in proposed fourteen pathways for different kinds of CC bond. Vibrational frequencies analysis and intrinsic reaction coordinate (IRC) calculations were carried out and the rate constants for all paths were calculated by using canonical transition state theory (CTST). The best and the worst paths and dominant products for this reaction were determined. Stability of the intermediates, transition sates and products was discussed. Results showed that in the first step of CH2N2 addition to sumanene and formation of corresponding transition state, hub position has the least and rim position has the most barrier energy. Also, for all types of CC bond, sumanene with a CH2 group as a bridge was formed and conversion of a sumanene hexagon to heptagon happened for all positions except spoke. Generally, diazomethane can add a CH2 group in the carbon chain, insert CH2 group as a bridge or add a CH3 group to the structure.

Mass and Stiffness Effects of Harnessing Cables on Structural Dynamics: Continuum Modeling

Dynamic analysis of satellite structures comprises an important part of their design. One such example is an inflatable deployable structure. Although prized for their small volume, mass, and subsequent launch costs, these structures are quite susceptible to disturbances in a space environment that can jitter their mission accuracy. Therefore, it is important to have models to accurately predict their vibrations response to these disturbances. One important aspect to include in these models is the effect of signal and power cables surrounding the host structure that has been traditionally ignored or accounted for using ad hoc models. Obtaining simple analytical solutions that can predict the dynamic behavior of these structures has numerous advantages for their vibrations control and modeling before their launch. Although damping plays an important role in the dynamics of these structures, the presented paper pertains only to the mass and stiffness effects of these cables. The structures are modeled as beam structures harnessed with cables and the governing partial differential equations of motion for different coordinates of vibrations, such as bending, longitudinal, and torsional modes, are derived for the harnessed structure. Two wrapping patterns for the cables are considered. Natural frequencies and the resultant frequency response functions are presented, and the results are compared to a finite element solution.

Homogenization Modeling of Periodically Wrapped String-Harnessed Beam Structures: Experimental Validation

High-flexibility, small-mass, and high-bandwidth controllers required for inflatable space missions need quite accurate models to predict higher-order dynamics of these structures. Some major components often ignored in dynamic analysis of space structures that result in model inaccuracies are space flight cables. The cables-to-payload-mass ratio can be about 20% in a traditional space structure; this number can increase significantly for inflatable structures due to their extremely light weights. As such, these cables can have significant impacts on the structural dynamics. The presented paper considers string-harnessed beam structures as a way to study the mass and stiffness effects of these cables. As a preliminary step, damping is ignored in the presented models. A homogenization technique is applied to develop the governing partial differential equation for the transverse bending coordinate of vibration of the string-harnessed beam structures. A periodic wrapping pattern is considered for the string throughout this paper. The frequency response functions for the continuum model are then compared to the experimental results, for which strong agreements are observed.

The repopulation of electronic states upon vibrational excitation of niobium carbide clusters

We study the infrared (IR) resonant heating of neutral niobium carbide clusters probed through ultraviolet photoionization spectroscopy. The IR excitation not only changes the photoionization spectra for the photon energies above the ionization threshold, but also modulates ion yield for energies significantly below it. An attempt to describe the experimental spectra using either Fowler's theory or thermally populated vibrational states was not successful. However, the data can be fully modeled by vibrationally and rotationally broadened discrete electronic levels obtained from Density Functional Theory (DFT) calculations. The application of this method to spectra with different IR pulse energies not only yields information about the excited electronic states in the vicinity of the HOMO level, populated by manipulation of the vibrational coordinates of a cluster, but also can serve as an extra indicator for the cluster isomeric structure and corresponding DFT-calculated electronic levels.

A global ab initio dipole moment surface for methyl chloride

A new dipole moment surface (DMS) for methyl chloride has been generated at the CCSD(T)/aug-cc-pVQZ(+d for Cl) level of theory. To represent the DMS, a symmetry-adapted analytic representation in terms of nine vibrational coordinates has been developed and implemented. Variational calculations of the infrared spectrum of CH3Cl show good agreement with a range of experimental results. This includes vibrational transition moments, absolute line intensities of the ν1, ν4, ν5 and 3ν6 bands, and a rotation–vibration line list for both CH335Cl and CH337Cl including states up to J=85 and vibrational band origins up to 4400cm−1. Across the spectrum band shape and structure are well reproduced and computed absolute line intensities are comparable with highly accurate experimental measurements for certain fundamental bands. We thus recommend the DMS for future use.

Effects of Molecular Symmetry on the Electronic Transitions in Carotenoids.

The aim of this work is the verification of symmetry effects on the electronic absorption spectra of carotenoids. The symmetry breaking in cis-β-carotenes and in carotenoids with nonlinear π-electron system is of virtually no effect on the dark transitions in these pigments, in spite of the loss of the inversion center and evident changes in their electronic structure. In the cis isomers, the S2 state couples with the higher excited states and the extent of this coupling depends on the position of the cis bend. A confrontation of symmetry properties of carotenoids with their electronic absorption and IR and Raman spectra shows that they belong to the C1 or C2 but not the C2h symmetry group, as commonly assumed. In these realistic symmetries all the electronic transitions are symmetry-allowed and the absence of some transitions, such as the dark S0 → S1 transition, must have another physical origin. Most likely it is a severe deformation of the carotenoid molecule in the S1 state, unachievable directly from the ground state, which means that the Franck-Condon factors for a vertical S0 → S1 transition are negligible because the final state is massively displaced along the vibrational coordinates. The implications of our findings have an impact on the understanding of the photophysics and functioning of carotenoids.

Infrared spectroscopy of ion-induced cross-linked sulfonated poly(ether ether ketone)

The dehydration of SPEEK-[H] (protonated sulfonated poly(ether ether ketone)) converts 3-fold symmetric (C3V) hydrated sulfonate sites to sulfonic acid sites with no local symmetry (C1). Like Nafion-[H], SPEEK-[H] C3V and C1 environments afford IR group modes (C3V,HF (1087 cm−1); C3V,LF (1026 cm−1) and C1,HF (1362 cm−1); C1,LF (904 cm−1)) due to the mechanical coupling of vibrational internal coordinates of an ether link with those of the sulfonate or sulfonic acid exchange site. C3V and C1 bands are inversely correlated during membrane hydration/dehydration. Hydrated SPEEK-[M] (M: Cu2+, Ni2+, Cd2+, Pb2+, Sr2+ or Ba2+) exhibits SPEEK-[H] C3V bands because cation waters of hydration preclude binding to the hydrated exchange site. When cation hydration spheres are thermally stripped at high vacuum, SPEEK-[M] C3V bands supplant SPEEK-[H] C3V bands, inducing SPEEK cross-linking. Incomplete cross-linking is evidenced by low intensities of SPEEK-[M] C1,HF bands. The 1362 cm−1 band intensities are inversely correlated with cation hydration enthalpies.

Relativistic theory of the Jahn-Teller effect: p-orbitals in tetrahedral and trigonal systems.

A relativistic generalization of Jahn-Teller theory is presented which includes spin-orbit coupling effects beyond low-order Taylor expansions in vibrational coordinates. For the example of a p-electron in tetrahedral and trigonal environments, the matrix elements of the Breit-Pauli spin-orbit-coupling operator are expressed in terms of the matrix elements of the electrostatic electronic potential. Employing expansions of the latter in invariant polynomials in symmetry-adapted nuclear coordinates, the spin-orbit induced Jahn-Teller coupling terms are derived for the T2 × (t2 + e) and (E + A) × (e + a) Jahn-Teller problems up to arbitrarily high orders. The linear G3/2 × (t2 + e) Jahn-Teller Hamiltonian of Moffitt and Thorson [Phys. Rev. 108, 1251 (1957)] for tetrahedral systems is generalized to higher orders in vibrational displacements. The Jahn-Teller Hamiltonians derived in the present work are useful for the interpolation and extrapolation of Jahn-Teller distorted potential-energy surfaces of molecules and complexes with heavy elements as well as for the calculation of vibronic spectra of such systems.

Optimizing Vibrational Coordinates To Modulate Intermode Coupling.

The choice of coordinate system strongly affects the convergence properties of vibrational structure computations. Two methods for efficient generation of improved vibrational coordinates are presented and justified by analysis of a model anharmonic two-mode Hessian and numerical computations on polyatomic molecules. To produce optimal coordinates, metrics which quantify off-diagonal couplings over a grid of Hessian matrices are minimized through unitary rotations of the vibrational basis. The first proposed metric minimizes the total squared off-diagonal coupling, and the second minimizes the total squared change in off-diagonal coupling. In this procedure certain anharmonic modes tend to localize, for example X-H stretches. The proposed methods do not rely on prior fitting of the potential energy, vibrational structure computations, or localization metrics, so they are unique from previous vibrational coordinate generation algorithms and are generally applicable to polyatomic molecules. Fitting the potential to the approximate n-mode representation in the optimized bases for all-trans polyenes shows that off-diagonal anharmonic couplings are substantially reduced by the new choices of coordinate system. Convergence of vibrational energies is examined in detail for ethylene, and it is shown that coupling-optimized modes converge in vibrational configuration interaction computations to within 1 cm(-1) using only 3-mode couplings, where normal modes require 4-mode couplings for convergence. Comparison of the vibrational configuration interaction convergence with respect to excitation level for the two proposed metrics shows that minimization of the total off-diagonal coupling is most effective for low-cost vibrational structure computations.

FALCON: A method for flexible adaptation of local coordinates of nuclei.

We present a flexible scheme for calculating vibrational rectilinear coordinates with well-defined strict locality on a certain set of atoms. Introducing a method for Flexible Adaption of Local COordinates of Nuclei (FALCON) we show how vibrational subspaces can be "grown" in an adaptive manner. Subspace Hessian matrices are set up and used to calculate and analyze vibrational modes and frequencies. FALCON coordinates can more generally be used to construct vibrational coordinates for describing local and (semi-local) interacting modes with desired features. For instance, spatially local vibrations can be approximately described as internal motion within only a group of atoms and delocalized modes can be approximately expressed as relative motions of rigid groups of atoms. The FALCON method can support efficiency in the calculation and analysis of vibrational coordinates and energies in the context of harmonic and anharmonic calculations. The features of this method are demonstrated on a few small molecules, i.e., formylglycine, coumarin, and dimethylether as well as for the amide-I band and low-frequency modes of alanine oligomers and alpha conotoxin.

Ionization energy and active cation vibrations of trans-2-fluorostyrene

We applied the two-color resonant two-photon mass-analyzed threshold ionization (MATI) technique to record the cation spectra of trans-2-fluorostyrene by ionizing via six intermediate vibronic levels. The adiabatic ionization energy was determined to be 69304±5cm−1. The distinct MATI bands at 67, 124, 242, 355, 737, 806, 833, and 993cm−1 were assigned to the active cation vibrations related to out-of-plane substituent-sensitive bending vibrations and in-plane ring deformation and bending motions. Many combination vibrations were also observed. Our experimental results suggest that the molecular geometry and vibrational coordinates of the trans-2-fluorostyrene cation in the D0 state resemble those of the neutral species in the S1 state.

Rotamers of 2, 5-Difluorophenol Studied Using Mass-Analyzed Threshold Ionization Spectroscopy

We applied resonant two-photon ionization (R2PI) and mass-analyzed threshold ionization (MATI) techniques to record the vibronic and cationic spectra of 2,5-difluorophenol. The distinct bands at 36448 and 36743 cm(-1) were confirmed as the origins of the S-1 <- S-0 So electronic transition of the cis and trans rotamers, respectively. The corresponding adiabatic ionization energies were found to be 71164 and 71476 cm(-1) for these two rotameric species. The observed spectral features mainly result from the in-plane ring deformation and substituent-sensitive bending vibrations. Spectral analysis suggests that the molecular geometry and vibrational coordinates of the cation in the Do state resemble those of the neutral species in the S-1 state for both cis and trans rotamers.