Highly excited vibrational levels of triatomic molecule N2O: U(4) algebraic model

In the U(4) algebraic framework, the triatomic molecules are of U₁(4) ? U₂(4) dynamical symmetry. A molecular Hamiltonian is constructed including the third‐order conbination of the invariant operators. Within this framework, the highly vibrational energy levels of the linear triatomic nitrous oxide molecule, including both bending and stretching vibrations, are studied. © 2006 Wiley Periodicals, Inc. Int J Quantum Chem, 2007     

Theoretical study of highly vibrational states of nonlinear triatomic molecules using Lie algebraic approach

The vibrational excitations of bent triatomic molecules are studied by using Lie algebra. The RMS error of fitting 30 spectroscopic data is 1.66 cm-1 for SO2. The results show that the expansion of a molecular algebraic Hamiltonian can well describe the experimental data. And the total vibrational levels can be calculated using this Hamiltonian. At the same time, the potential energy surface can also be obtained with the algebraic Hamiltonian.     

A Lie group method for molecular rovibrational spectra via the broken symmetry of U(r)(2)⊗U(υ)(4)

A special group chain that is appropriate for describing the rovibrational spectra of linear triatomic molecules with respect to both the vibration and the rotation of molecules as harmonic oscillators is given, and the corresponding Hamiltonian is constructed. The eigenvalue expression of the Hamiltonian is similar to the formula commonly used to calculate the rovibrational spectra of linear triatomic molecules. This method eliminates the physical uncertainty brought about by a variety of group chains. The relationships between parameters in the present expression and those in the commonly used expressions are given. © 2001 John Wiley & Sons, Inc. Int J Quant Chem 83: 53–59, 2001     

Model calculations for the predissociative excitation of CS2

A collinear model for predissociation of linear triatomic molecules is presented. A very steep repulsive potential for CS (A) + S is obtained by fitting the experimental results from the dissociation of CS₂ at various excitation energies. Qualitative agreement has also been obtained for the rotational energy distribution of the product fragment. The role of the interfragment effect in determining the CS (A) vibrational distributions is discussed.     

Variational calculation of vibrational energies of triatomic molecules using SCF optimized modes

A self-consistent field optimization of the vibrational coordinates for nonlinear triatomic molecules is presented. The optimal coordinates are obtained by making a three-dimensional rotational transformation of the normal modes and determining the rotation angles as those for which the SCF energy is stationary. The utility of the optimized coordinates in full variational calculations of vibrational energies is studied for the molecules of H₂O, O₃, H₂D⁺, H₂T⁺, and D₂T⁺. For H₂O and O₃, the optimization procedure leads to the local mode representation. It is shown that the use of the optimal coordinates in variational calculations allows a large reduction of the dimension of the Hamiltonian matrix to be diagonalized in order to reach convergence.     

Separation of the vibrational,rotational, and translational motions of polyatomic molecules using curvilinear vibrational coordinates

A new method is suggested for separating the vibrational, rotational, and translational motions of polyatomic molecules using curvilinear vibrational coordinates that are linear with respect to the natural vibrational coordinates. It is shown that, in this case, Coriolis interactions between the vibrational and rotational motions are absent. The solutions of the anharmonic vibrational-rotational problems in the curvilinear and linear vibrational coordinates are compared. The absence of Coriolis interactions between the vibrational and rotational motions in the curvilinear vibrational coordinates is proved numerically. The same conclusion is additionally supported by calculations of the anharmonic vibrational energy levels for the H₂O, H₂S, NO₂, SO₂, and ClO₂ molecules in the linear and curvilinear vibrational coordinates using the Hamiltonian designed in the curvilinear vibrational coordinates with and without Coriolis vibrational-rotational interactions. Volgograd Pedagogical University. Translated fromZhurnal Strukturnoi Khimii, Vol. 36, No. 2, pp. 239–254, March–April, 1995. Translated by I. Izvekova     

Application of Lie algebraic method to the calculation of rotational spectra for linear triatomic molecules

The Hamiltonian describing rotational spectra of linear triatomic molecules has been derived by using the dynamical Lie algebra of symmetry group U1(4) U2(4). After rovibrational interactions being considered, the eigenvalue expression of the Hamiltonian has the form of term value equation commonly used in spectrum analysis. The molecular rotational constants can be obtained by using the expression and fitting it to the observed lines. As an example, the rotational levels of v2 band for transition (02°0-0110) of molecules N2O and HCN have been fitted and the fitting root-mean-square errors (RMS) are 0.00001 and 0.0014 cm-1, respectively.     

Triatom-triatom collisions: Fixed angle close-coupling study of vibrational excitation in the 12CO2+13CO2 system

A close-coupling approach to the calculation of quantal vibrational transition probabilities for the fixed angle scattering of a linear triatomic molecule with another linear triatomic molecule is described. The method is applied to the ¹²CO₂+¹³C0₂ collisional system. For a calculated inelastic transition probability to have an appreciable magnitude, it is found that the amount of energy transferred in a transition must be very small and just one quantum of energy must be exchanged between either the symmetric stretch or the asymmetric stretch vibrational modes of ¹²C0₂ and ¹³CO₂. For collisional energies away from threshold, the probabilities for transitions involving the symmetric stretch ¹²CO₂ and ¹³CO₂ modes are insensitive to long range multipole terms in the potential energy surface, while the probabilities for energy exchange between the asymmetric stretch modes are considerably diminished when the long range terms are removed from the potential energy surface. A brief discussion is presented on the possibilities of extending the technique to the calculation of vibrational excitation cross sections for three-dimensional triato—triatom collisions.     

Rovibrational interactions in linear triatomic molecules: a theoretical study in curvilinear vibrational coordinates

Variational solution of the rovibrational problem in curvilinear vibrational coordinates has been implemented and used to investigate the nuclear motions in several linear triatomic molecules, like HCN, OCS, and HCP. The dependence of the rovibrational energy levels on the rotational quantum numbers and the l-doubling has been studied. Two approximations to the rovibrational Hamiltonian have been examined, depending on the level of truncation of the potential energy operator. It turns out that the truncation after the fifth order in the potential is sufficient to produce vibrational energies of high accuracy. An interesting feature of the present formulation of the problem in terms of the curvilinear vibrational coordinates is the explanation of the l-doubling of the rovibrational levels, which in this picture is interpreted as the result of the inequivalency of the average rotational constants in mutually perpendicular planes, rather than as the effect of the Coriolis-type interactions between the vibrational and rotational motions. The present theoretical results are compared with the available experimental data from high-resolution spectroscopy, as well as with other ab initio calculations.     

Definitive heat of formation of methylenimine,CH2NH,and of methylenimmonium ion,CH2NH2+, by means of W2 theory

A long‐standing controversy concerning the heat of formation of methylenimine has been addressed by means of the W2 (Weizmann‐2) thermochemical approach. Our best calculated values, ΔH°_f,298(CH₂NH) = 21.1±0.5 kcal/mol and ΔH°_f,298(CH₂NH₂⁺) = 179.4±0.5 kcal/mol, are in good agreement with the most recent measurements but carry a much smaller uncertainty. As a byproduct, we obtain the first‐ever accurate anharmonic force field for methylenimine: upon consideration of the appropriate resonances, the experimental gas‐phase band origins are all reproduced to better than 10 cm^?1. Consideration of the difference between a fully anharmonic zero‐point vibrational energy and B3LYP/cc‐pVTZ harmonic frequencies scaled by 0.985 suggests that the calculation of anharmonic zero‐point vibrational energies can generally be dispensed with, even in benchmark work, for rigid molecules. © 2001 John Wiley & Sons, Inc. J Comput Chem 22: 1297–1305, 2001     

Discrete variable representation method applied to the determination of rotation-vibration bound states of NO2

The discrete variable representation method is applied to the determination of the rotation-vibration energy levels of the fundamental electronic state of NO₂. The Hamiltonian is expressed in Johnson hyperspherical coordinates and developed on a DVR basis for each internal coordinate, while parity-adapted linear combinations of Wigner functions are used to describe the rotational motion. The diagonalization of the Hamiltonian matrix is performed using the Lanczos algorithm for large symmetric and Hermitian matrices. Results for rovibrational states up to J = 11 for the first five vibrational energy levels are presented. © 1997 John Wiley & Sons, Inc.     

The calculation of vibrational energy levels of polyatomic molecules including anharmonic effect using contact transformation perturbation method

Using contact transformation perturbation method based on the Taylor expansion of the potential energy function in terms of dimensionless normal coordinates up to sixth‐order, the vibrational energy levels in terms of force constants are derived. The contact transformation theory has been applied to simplify the calculation of perturbation effects. To calculate the second‐order vibrational energy correction, the third and fourth‐order terms of potential function have been placed in the first‐order perturbation Hamiltonian and the second‐order Hamiltonian contains hexatic ones. We present expressions which give relations between the fourth‐ and sixth‐order terms in dimensionless normal coordinates of the potential and the anharmonicity coefficients. For illustration, a set of vibrational energies levels of SO₂, and H₂O molecules including anharmonic effects has been calculated. © 2013 Wiley Periodicals, Inc.     

V—V,V—R,T transfer in triatomic molecules. Results for ONF

The laser-induced fluorescence technique is applied to study vibrational energy transfer in pure ONF. Different vibrational modes are excited using a TEA CO₂ laser and the rise and fall of ν₁, ν₂, and (ν₁ + ν₃) fluorescence is detected. These measurements yield a detailed picture of V—V exchange in the region of the fundamentals and V—R,T transfer to rotational and translational degrees of freedom. The relaxation behavior of ONF is compared with that of ONCI and other triatomic molecules.     

NeI2 Photofragmentation Dynamics Through Quasiclassical and Semiclassical Studies

The triatomic system NeI₂ is studied under the consideration that the diatom is found in an excited electronic state (B). The vibrational levels (v=13, …, 23) are considered within two well-known theoretical procedures: quasi-classical trajectories (QCT), where the classical equations of motion for nuclei are solved on a single potential energy surface (PES), and the trajectory surface hopping (TSH) method, where the same are solved in a bunch of crossed vibrational PES (diabatic representation). The trajectory surface hopping fewest switches (TSHFS) is implemented to minimize the number of hoppings, thus allowing the calculations of hopping probability between the different PES's, and the kinetic mechanism to track the dissociation path. From these calculations, several observables such as, the lifetimes, vibrational and rotational energies (I₂), dissociation channels, are obtained. Our results are compared with previous experimental and theoretical work.     

Potential energy surface and highly excited vibrational lines of NO2 via algebraic approach

The algebraic Hamiltonian of NO₂ is optimized using U(4) algebra via fitting to 102 observed vibrational lines. The RMS error of the fitting is 2.39 cm^?1. We calculated highly excited vibrational energy levels using this optimized Hamiltonian, and then obtained the potential energy surface for the electronic ground state by using the classical limit of the U(4) algebraic Hamiltonian. We also calculated the dissociation energies, the force constants etc. Our results are in good agreement with the other theoretical results. © 2008 Wiley Periodicals, Inc. Int J Quantum Chem, 2008     

Statistical properties of the energies and electric dipole moments of the bound vibrational states of the system HCO/COH

From the ab initio calculated three-dimensional adiabatic double-minimum potential energy surface of the HCO⁺/COH⁺ system and the corresponding dipole moment surface the energies of all bound vibrational states and their effective dipole moments are determined applying the Suttcliffe–Tennyson Hamiltonian for triatomic molecules. The energy and dipole data are analysed in terms of statistical methods such as the density of states approach and the nearest-neighbor level spacing distribution (NNSD). Special effort is put into investigating the effect of the tunnelling motion across the isomerization barrier on the NNSD representations.     

Potential energy surface for linear triatomic molecules: An algebraic method

Recently, we proposed a new transformation between the angle of canonical coordinates and the bond angle to describe the bending motion in Potential Energy Surfaces (PES) of bent triatomic molecules. In this work we extend the transformation to include linear triatomic molecules. Results for the linear triatomic molecule N₂O are reported.     

Theoretical study of the potential-energy surface of C2NP

 The B3LYP/6-311G(d) and CCSD(T)/6-311G(2df) (single-point) methods have been used to investigate the singlet potential energy surface of C₂NP, in which seven stationary isomers and seventeen interconversion transition states are involved. At the final CCSD(T)/6-311G(2df)//B3LYP6-311G(d) level with zero-point vibrational energy correction the lowest-lying isomer is a linear NCCP followed by two linear CNCP isomers at 23.9  and CCNP at 65.8 kcal mol⁻¹, respectively. The three isomers are kinetically very stable towards both isomerization and dissociation, and CCNP is even more kinetically stable than CNCP – by 14.3 kcal mol⁻¹ despite its high energy. Further comparative calculations were performed at the QCISD and QCISD(T) levels with the 6-311G(d) and 6-311G(2d) basis sets to obtain more reliable structures and spectroscopy for the three isomers. The calculated bond lengths, rotational constant, and dipole moment for NCCP were in close agreement with the experimentally determined values. Finally, similarities and discrepancies between the potential energy surface of C₂NP and those of the analogous species C₂N₂ and C₂P₂ were compared. The results presented in this paper might be helpful for future identification of the two still unknown yet kinetically very stable isomers CNCP and CCNP, both in the laboratory and in interstellar space. Received: 3 January 2001 / Accepted: 6 June 2001 / Published online: 30 October 2001     

On the interaction of Mo and Mo2 with NH3, C2H4, and C3H6

The reactivity of Mo and Mo₂ with ammonia, ethene, and propene molecules has been investigated by using Density Functional Theory. Different gradient‐corrected and hybrid exchange‐correlation functionals have been employed. Coordination modes, binding energies, geometrical structures, vibrational frequencies have been computed and compared with the available experimental counterparts. The results obtained show that the molybdenum atom is able to react with C₂H₄ and C₃H₆, and binds weakly with NH₃. The dimer Mo₂ gives a stable complexes with ammonia, ethene, and propene. For the Mo₂NH₃ complex, all the employed levels of theory give binding energies in good agreement with the experimental value, while in the case of the MoC₂H₄ system, the use of model core potentials coupled with gradient‐corrected exchange‐correlation functionals overestimates the binding energies. For MoC₃H₆, Mo₂C₂H₄, and Mo₂C₃H₆ we predict a binding energy of 14–15, 20–24, and 18–20 kcal/mol, respectively. © 2001 John Wiley & Sons, Inc. J Comput Chem 22: 1557–1564, 2001     

Vibrational spectra and assignments of 2-phenylethanol and 2-phenoxyethanol

The structural stability of 2-phenyl- and 2-phenoxyethanols were investigated at the DFT-B3LYP/6-311G**, MP2 and MP4(SDQ) levels of theory. From the calculations at the three levels of theory 2-phenylethanol and 2-phenoxyethanol were predicted to exist predominantly in non-planar gauche conformations. For 2-phenylethanol the lowest energy Gg1 structure was predicted to be stabilized by an interaction between the hydroxyl H atom and the phenyl ring. For 2-phenoxyethanol the Ggg1 structure was predicted to be strongly stabilized by dipolar interactions between the hydroxyl H atom and the phenoxy O atom of the alcohol. For both alcohols the planar trans structure with minimum steric interactions between the CH₂ groups was predicted to be significantly higher in energy than the ground state gauche structure of the alcohols. The dipolar interactions are reported to play more important role than steric ones in stabilizing the molecules. The vibrational frequencies of each of the two alcohols in its lowest energy gauche structure were computed at the B3LYP level and tentative vibrational assignments were made for their normal modes on the basis of the calculated and experimental data.