A simple curvilinear internal coordinate model for vibrational energy levels

Novel Criteria to Provide a Locality/Normality Degree in Molecules and Their Relevance in Physical Chemistry

In contrast to the traditional analysis of molecules using local mode behavior, where the degree of locality is given through a function in terms of Morse potential parameters, new criteria for locality/normality (LN) suitable for application to any molecular system are proposed. The approach is based on analysis of the connection between the algebraic normal and local mode representations. It is shown that both descriptions are equivalent as long as the polyad (total number of quanta) in the local representation is not conserved. The constraint of a local polyad conservation naturally provides a criterion for assigning an LN degree in quantitative form, without an analogue in configuration space. The correlation between the different parameters reveals the physical properties of molecules. A clear connection between the LN degree (based on the fundamentals) and spectroscopic properties is also presented, suggesting a promising approach for identifying mixtures of isotopologues.

Ab initio potential energy surface and vibration-rotation energy levels of sulfur dioxide

An accurate potential energy surface of sulfur dioxide, SO₂ , in its ground electronic state X∼ 1A1 has been determined from ab initio calculations using the coupled-cluster approach in conjunction with the correlation-consistent basis sets up to septuple-zeta quality. The results obtained with the conventional and explicitly correlated coupled-cluster methods are compared. The role of the core-electron correlation, higher-order valence-electron correlation, scalar relativistic, and adiabatic effects in determining the structure and dynamics of the SO₂ molecule is discussed. The vibration-rotation energy levels of the ³² SO₂ and ³⁴ SO₂ isotopologues were predicted using a variational approach. It was shown that the inclusion of the aforementioned effects was mandatory to attain the "spectroscopic" accuracy. © 2017 Wiley Periodicals, Inc.

The OH-Initiated Oxidation of CS2 in the Presence of NO: FTIR Matrix-Isolation and Theoretical Studies

We studied the photochemistry of the carbon disulfide-nitrous acid system with the help of Fourier transform infrared (FTIR) matrix isolation spectroscopy and theoretical methods. The irradiation of the CS2···HONO complexes, isolated in solid argon, with the filtered output of the mercury lamp (λ > 345 nm) was found to produce OCS, SO2, and HNCS; HSCN was also tentatively identified. The (13)C, (15)N, and (2)H isotopic shifts as well as literature data were used for product identifications. The evolution of the measured FTIR spectra with irradiation time and the changes in the spectra after matrix annealing indicated that the identified molecules are the products of different reaction channels: OCS being a product of another reaction path than SO2 and HNCS or HSCN. The possible reaction channels between SC(OH)S/SCS(OH) radicals and NO were studied using DFT/B3LYP/aug-cc-pVTZ method. The SC(OH)S and/or SCS(OH) intermediates are formed when HONO attached to CS2 photodissociates into OH and NO. The calculations indicated that SC(OH)S radical can form with NO two stable adducts. The more stable SC(OH)S···NO structure is a reactant for a simple one-step process leading to OCS and HONS molecules. An alternative, less-stable complex formed between SC(OH)S and NO leads to formation of OCS and HSNO. The calculations predict only one stable complex between SCS(OH) radical and NO, which can dissociate along two channels leading to HNCS and SO2 or HSCN and SO2 as the end products. The identified photoproducts indicate that both SC(OH)S and SCS(OH) adducts are intermediates in the CS2 + OH + NO reaction leading to different reaction products.

A periodic orbit bifurcation analysis of vibrationally excited isotopologues of sulfur dioxide and water molecules: symmetry breaking substitutions

Theoretical predictions and assignment of highly excited vibrational states and their organization is one of the most important challenges in molecular spectroscopy. A systematic procedure to investigate such problems is locating the principal families of periodic orbits that emanate from the stationary points of the molecule and then following their evolution with the total energy. This results in constructing continuation/bifurcation diagrams that assist in locating the critical bifurcation energies and to discover new types of vibrational modes. Another parameter that may influence the dynamics of a molecule is isotopic mass substitution. In this article, we investigate the effect of symmetry breaking by isotopic mass substitution of triatomic molecules with C(2v) symmetry in classical and quantum dynamics. Sulfur dioxide and water molecules in their ground electronic state are studied by employing accurate potential energy surfaces. Continuation/bifurcation diagrams of periodic orbits are constructed by varying the energy and the mass of one oxygen atom of sulfur dioxide and one hydrogen atom of a water molecule. The transition from normal-to-local mode vibrations is studied in terms of a pitchfork to a center-saddle elementary bifurcation of periodic orbits. The results presented in this article aim to help the assignment of experimentally obtained spectra.

Optimal internal coordinates, vibrational spectrum, and effective Hamiltonian for ozone

In this paper the authors use the optimal internal vibrational coordinates previously determined for the electronic ground state of the ozone molecule to study the vibrational spectrum of the molecule employing the second empirical potential energy surface calculated by Tyuterev et al. [Chem. Phys. Lett. 316, 271 (2000)]. First, the authors compute variationally all the bound vibrational energy levels of the molecule up to the dissociation limit and state the usefulness of the optimal coordinates in this respect, which allows us to converge all the bound levels using relatively small anharmonic basis sets. By analyzing the expansion coefficients of the wave functions, they show then that a large portion of the vibrational spectrum of O3 can be structured in nearly separable polyadic groups characterized by the polyad quantum number N=n1+n2+n(theta) corresponding to the optimal internal coordinates. Accordingly, they determine an internal effective vibrational Hamiltonian for O3 by fitting the effective Hamiltonian parameters to the experimental vibrational frequencies, using as input parameters in the fit those extracted from an analytical second-order Van Vleck perturbation theory calculation. It is finally shown that the internal effective Hamiltonian thus obtained accurately describes the vibrational spectrum of ozone in the low and medium energy regimes.

Infrared spectroscopy of hydrogen-bonded CHCl3-SO2 in the gas phase

A molecular association between chloroform and sulfur dioxide in the gas phase at room temperature was studied by Fourier transform infrared spectroscopy. Since the intensity of the CH-stretching fundamental vibration of monomer chloroform is very weak but much stronger upon complexation, a simple subtraction procedure isolated the CH-stretching vibration spectrum of the complex. The presence of a 1:1 complex was confirmed by two dilution series, where the monomer concentrations were varied. The molecular association manifested itself as a shift of the peak absorbance of the CH-stretching vibration of CHCl3-SO2 by +7 cm(-1) and of the CD-stretching vibration of CDCl3-SO2 by +5 cm(-1) to higher wave numbers compared to monomer chloroform, accompanied by a considerable broadening of the band contour. In agreement with previous ab initio calculations, this indicates a "blueshifting" or more appropriately, a "C-H contracting" hydrogen bond between chloroform and sulfur dioxide. An estimate of the complex concentration was made based on ab initio calculations for the integrated band strength and the measured spectrum. With this estimate, the equilibrium constant Kp (295 K)=0.014 (po=10(5) Pa) for the dimerization was calculated, providing one of the very few cases where the formation of a hydrogen-bonded gas phase complex at room temperature could be quantitatively studied by infrared spectroscopy.

Simulation of inversion motion and N–H stretching overtone spectra of aniline

A curvilinear internal coordinate Hamiltonian is used to simulate the N-H stretching overtone spectra and the associated inversion splittings in aniline. A simple local mode type model is applied to the N-H stretching and H-N-H bending modes. Geometric algebra is employed to derive the kinetic energy operator for the large amplitude inversion motion. Electronic structure calculations at the Moller-Plesset second order perturbation theory and correlation consistent aug-cc-pVTZ basis set level are used to obtain model parameters, some of which have been optimized with the least-squares method using experimental vibrational term values as data. The observed N-H stretching overtone vibrational levels and the inversional tunneling splittings are well reproduced with our approach.

On the use of optimal internal vibrational coordinates for symmetrical bent triatomic molecules

The use of generalized internal coordinates for the variational calculation of excited vibrational states of symmetrical bent triatomic molecules is considered with applications to the SO2, O3, NO2, and H2O molecules. These coordinates depend on two external parameters which can be properly optimized. We propose a simple analytical method to determine the optimal internal coordinates for this kind of molecules based on the minimization with respect to the external parameters of the zero-point energy, assuming only quadratic terms in the Hamiltonian and no quadratic coupling between the optimal coordinates. The optimal values of the parameters thus obtained are shown to agree quite well with those that minimize the sum of a number of unconverged energies of the lowest vibrational states, computed variationally using a small basis function set. The unconverged variational calculation uses a basis set consisting of the eigenfunctions of the uncoupled anharmonic internal coordinate Hamiltonian. Variational calculations of the excited vibrational states for the four molecules considered carried out with an increasing number of basis functions, also evidence the excellent convergence properties of the optimal internal coordinates versus those provided by other normal and local coordinate systems.

A realistic double many-body expansion potential energy surface for SO2(X1A') from a multiproperty fit to accurate ab initio energies and vibrational levels

A single-valued double many-body expansion potential energy surface (DMBE I) recently obtained for the ground electronic state of the sulfur dioxide molecule by fitting correlated ab initio energies suitably corrected by scaling the dynamical correlation energy is now refined by fitting simultaneously available spectroscopic levels up to 6886 cm(-1) above the minimum. The topographical features of the novel potential energy surface (DMBE II) are examined in detail, and the method is emphasized as a robust route to fit together state-of-the-art theoretical calculations and spectroscopic measurements using a single fully dimensional potential form.

The H2S Spectrum around 0.7 µm

The overtone spectrum of H2S has been recorded by intracavity laser spectroscopy in the 14100-14400 cm-1 spectral region. The rovibrational analysis was performed allowing one to assign not only lines involving the pair of interacting states {(402), (303)} ({(60(+), 0), (60(-), 0)} in local mode notation), but also lines involving the interacting states {(322), (223)} ({50(+), 2), (50(-), 2)} in local mode notation). Indeed, apart from the strong H22 interactions that link the rotational levels of the states (60(+/-), 0) on the one hand, and the rotational levels of the states (50(+), 2) on the other hand, we observe that the rotational levels of the two pairs of states interact strongly through anharmonic and Coriolis-type resonances. These resonances transfer intensity to lines involving the (50(+), 2) pair of states. Altogether 80 rotational upper-state levels have been observed and reproduced satisfactorily using an Hamiltonian matrix that takes explicitly into account the various interactions and assumes the same vibrational energy and rotational constants for the two components of the local mode pairs. The following band centers have been obtained: nu0 (60(+), 0) = 14291.122 cm-1 and nu0 (50(+/-), 2) = 14284.705 cm-1. Finally a local mode-type behavior is evidenced by the values of the Hamiltonian constants, and refined vibrational local mode parameters are obtained. Copyright 1998 Academic Press.