Six-dimensional tunneling dynamics of internal rotation in hydrogen peroxide molecule and its isotopomers

The six-dimensional torsion-vibration Hamiltonian of the H₂O₂ molecule and its H/D- and ¹⁸O/¹⁶O-isotopomers is derived. The Hamiltonian includes the kinetic energy operator, which depends on the tunneling coordinate, and the potential energy surface represented as a quartic polynomial with respect to the small-amplitude transverse coordinates. Parameters of the Hamiltonian were obtained from DFT calculations of the equilibrium geometries, eigenvectors, and eigenfrequencies of normal vibrations at the stationary points corresponding to the ground state and both the cis- and trans-transition states, carried out with the B3LYP density functional and 6-311+G(2d,p) basis set. The quantum dynamics problem is solved using the perturbative instanton approach generalized for the excited states situated above the barrier top. Vibration-tunneling spectra are calculated for the ground state and low-lying excited states with energies below 2000 cm^–1. Strong kinematic and squeezed potential couplings between the large-amplitude torsional motion and bending modes are shown to be responsible for the vibration-assisted tunneling and for the dependence of tunneling splittings on the quantum numbers of small-amplitude transverse vibrations. Mode-specific isotope effects are predicted.     

Multidimensional tunneling dynamics of proton transfer in malonaldehyde molecule and its isotopomers

The twenty-one-dimensional Hamiltonian of malonaldehyde molecule and a number of its isotopomers (H/D, ¹³C/¹²C) was reconstructed in the low-energy region (<3000 cm^–1). Parameters of the Hamiltonian were obtained from quantum-chemical calculations of the energies, equilibrium geometries, and eigenvectors and eigenfrequencies of normal vibrations at the stationary points corresponding to the ground state and transition state. Despite substantial variation of the barrier height calculated using different quantum-chemical methods (from 2.8 to 10.3 kcal mol^–1), the corresponding potential energy surfaces can be matched with high accuracy by scaling only one parameter (the semiclassical parameter , which defines the scales of potential, energy, and action). Scaling invariance allows optimization of the Hamiltonian in such a way that the calculated ground-state tunneling splitting coincides with the experimental value. The corresponding potential barrier height is estimated at 4.34±0.4 kcal mol^–1. The quantum dynamics problem was solved using the perturbative instanton approach without reducing the number of degrees of freedom. The role of all transverse vibrations in proton tunneling is characterized. Vibration-tunneling spectrum is calculated for the ground state and low-lying excited states and mode-specific isotope effects are predicted.     

Conformational stability of peroxynitric acid molecule and the barriers to internal rotation about the O−O and N−O bonds

The structure of conformers and potential curves of the internal rotation (PCR) about the O?O and N?O bonds in peroxynitric acid (PNA) were calculated by the unrestricted Hartree-Fock-Roothaan method. The standard valence-split 6–31G and 6–31G^* basis sets were used. The presence of two maxima on every curve has been shown. To refine the values of barriers to the internal rotation in the regions of minima and maxima of PCR, calculations taking into account the electron correlation energy have been carried out at the second- and fourth-order Møller-Plesset level of perturbation theory (MP2 and MP4, respectively). At the MP4/6-61G^* level of approximation, the barriers to the rotation about the O?O bond are equal to 8.6 kJ mol^?1 and 14.7 kJ mol^?1, and both barriers to the rotation about the N?O bond are equal to 33.5 kJ mol^?1. The results are compared with those published for PCR in hydrogen peroxide and peroxynitric acid.     

Vibrational stimulation of the coherent tunneling transition in the cyclopentanone molecule

The tunneling interconversion of the cyclopentanone molecule, which leads to the appearance of tunneling doublets in the microwave spectrum of the system, is studied. The dynamics of interconversion is described by two generalized coordinates, one of which corresponds to bending (non-tunneling promoting mode), while the other of which corresponds to twisting of the molecular plane (tunneling coordinate). The coupling between two coordinates is symmetric. A method for quasi-classical calculation of the wave functions in the tunneling region and of the tunneling splittings of the vibrationally excited states in a two-dimensional potential with symmetric coupling is proposed. The tunneling spectrum of cyclopentanone is calculated. It agrees well with the experimental one, and the tunneling splitting increases by 140 times when the transverse quantum number goes from 0 to 6. The dynamic effect of the vibrationally assisted tunneling is shown to be due to the increase in the width of the tunneling channel with the quantum number of bending mode, as well as to the simultaneous shortening of the tunneling distance. The transition state geometry is found using the wave function at the dividing line of the potential.Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 12, pp. 2098–2105, December, 1994.This work was supported by the Russian Foundation for Basic Research (Project 94-03-08863). The authors express their gratitude to W. Miller for helpful discussions and to H. Nakamura for a preprint of their work.     

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 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 ³²SO₂ and ³⁴SO₂ 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.     

Double proton migrations in the associates of formic acid with nitrous,nitric, orthophosphoric,and sulfuric acids

Mechanisms of the proton transfer in dimeric associates of formic acid with nitrous, nitric, orthophosphoric, and sulfuric acids were studied by theab initio (HF/6-31G^**) method. The mechanism of the cooperative (concerted or one-step) proton transfer was shown to occur in all cases. The calculated activation barriers of the proton transfer reactions for the associates investigated are equal to 19.9, 14.2, 13.3, and 10.7 kcal mol^–1, respectively.Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 9, pp. 2184–2189, September, 1996.     

Specificity of internal rotation in aldehydes with three-membered rings

The results of anharmonic calculations of low-frequency vibrations of aldehyde molecules containing a three-membered cycle with a π-bond are presented. The theoretical exploration of the conformational behavior and geometrical structure of two related molecules is carried out and potential energy surface sections along the coordinates of internal rotation and non-planar vibration close in frequency are constructed and analyzed. The possibility of kinematic coupling of these two vibrations and the complexity of their forms are especially considered.     

Ab initio potential energy surface and vibration‐rotation energy levels of beryllium monohydroxide

The accurate potential energy surface of beryllium monohydroxide, BeOH, in its ground electronic state has been determined from ab initio calculations using the coupled‐cluster approach in conjunction with the correlation‐consistent core‐valence basis sets up to septuple‐zeta quality. The higher‐order electron correlation, scalar relativistic, and adiabatic effects were taken into account. The BeOH molecule was confirmed to be bent at equilibrium, with the BeOH angle of 141.2° and the barrier to linearity of 129 cm⁻¹. The vibration‐rotation energy levels of the BeOH and BeOD isotopologues were predicted using a variational approach and compared with recent experimental data. The results can be useful in a further analysis of high‐resolution vibration‐rotation spectra of these interesting species. © 2016 Wiley Periodicals, Inc.     

Ab initio potential energy surface and vibration‐rotation energy levels of silicon dicarbide,SiC2

The accurate ground‐state potential energy surface of silicon dicarbide, SiC₂, has been determined from ab initio calculations using the coupled‐cluster approach. Results obtained with the conventional and explicitly correlated coupled‐cluster methods were compared. The core‐electron correlation, higher‐order valence‐electron correlation, and scalar relativistic effects were taken into account. The potential energy barrier to the linear SiCC configuration was predicted to be 1782 cm^?1. The vibration‐rotation energy levels of the SiC₂, ²⁹SiC₂, ³⁰SiC₂, and SiC¹³C isotopologues were calculated using a variational method. The experimental vibration‐rotation energy levels of the main isotopologue were reproduced to high accuracy. In particular, the experimental energy levels of the highly anharmonic vibrational ν₃ mode of SiC₂ were reproduced to within 6.7 cm^?1, up to as high as the v₃ = 16 state.     

Ab initio study on the internal rotation of five π-conjugated hydrocarbons at MP2 level

The potential-energy curves of internal rotation were calculated for 1,3-butadiene at the MP2/6-311G** level, for isoprene and 1,3-pentadiene at the MP2/6-311G* level, and for 2,3-dimethyl-1,3-butadiene and styrene at the MP2/6-31G* level. The geometries of the energy minima (stable conformers) and maxima (transition states) on the curves are completely optimized. For butadiene and its methyl derivatives, two stable rotamers, s-trans and gauche conformers, are obtained. s-trans forms have the lowest energies and gauche conformers twisted by 39.9°–48.3° around the central bond of the butadiene skeleton are, on average, 9.8 kJ/mol above the trans forms. s-cis forms are rotational transition states. The computed gauche–cis barriers range from 4.30 to 11.70 kJ/mol. The regular effects of methyl substitutions at the end and central carbons are found. For styrene, the planar form is calculated to be a saddle point which is only about 1 kJ/mol higher in total energy than a twisted minimum, in which the torsional angle between the phenyl and vinyl planes is 27.4°. © 1998 John Wiley & Sons, Inc. Int J Quant Chem 69: 659–667, 1998     

Skeletal Torsion Tunneling and Methyl Internal Rotation: The Coupled Large Amplitude Motions in Phenyl Acetate

The rotational spectrum of phenyl acetate, CH₃COOC₆H₅, is measured using a free jet absorption millimeter-wave spectrometer in the range from 60 to 78 GHz and two pulsed jet Fourier transform microwave spectrometers covering a total frequency range from 2 to 26.5 GHz. The features of two large amplitude motions, the methyl group internal rotation and the skeletal torsion of the CH₃COO group with respect to the phenyl ring C₆H₅ (tilted at about 70°), characterize the spectrum. The vibrational ground state is split into four widely spaced sublevels, labeled as A0, E0, A1, and E1, each of them with its set of rotational transitions and with additional interstate transitions. A global fit of the line frequencies of the four sublevels leads to the determination of 51 spectroscopic parameters, including the ΔE_A0/A1 and ΔE_E0/E1 vibrational splittings of ~36.4 and ~33.5 GHz, respectively. The V₃ barrier to methyl internal rotation (~136 cm⁻¹) and the skeletal torsion B₂ barrier to the orthogonality of the two planes (~68 cm⁻¹) are deduced.     

Separation of variables and search algorithm for internal rotation coordinates and kinematic coefficients in the theory of nuclear motions in polyatomic molecules

The construction algorithm is proposed for the internal rotation coordinates in polyatomic molecules. It is based on the properties of the matrix of kinematic coefficients when an excessive system of natural coordinates is introduced. The approximations providing the separation of variables are considered. The exact form of the kinetic energy operator is given.     

Internal Conversion of Vibrational Quanta in the Inelastic Electron Tunneling

A scheme of direct experimental observation of the internal conversion of vibrational quanta is suggested; this effect occurs during the electron tunneling in bridge contacts.     

Statistical thermodynamics of internal rotation in a hindering potential of mean force obtained from computer simulations

A method of statistical estimation is applied to the problem of one-dimensional internal rotation in a hindering potential of mean force. The hindering potential, which may have a completely general shape, is expanded in a Fourier series, the coefficients of which are estimated by fitting an appropriate statistical-mechanical distribution to the random variable of internal rotation angle. The function of reduced moment of inertia of an internal rotation is averaged over the thermodynamic ensemble of atomic configurations of the molecule obtained in stochastic simulations. When quantum effects are not important, an accurate estimate of the absolute internal rotation entropy of a molecule with a single rotatable bond is obtained. When there is more than one rotatable bond, the "marginal" statistical-mechanical properties corresponding to a given internal rotational degree of freedom are reduced. The method is illustrated using Monte Carlo simulations of two public health relevant halocarbon molecules, each having a single internal-rotation degree of freedom, and a molecular dynamics simulation of an immunologically relevant polypeptide, in which several dihedral angles are analyzed.     

Theoretical model of internal rotation in monosubstituted derivatives of furfural

The present work explores the effect of substitution in all free positions of furfural on conformational preferences of formyl group by using ab-initio calculations at the MP2/6-31G(p,d) level of theory. Theoretical modeling was made in vacuo. The selected substituents were -CH(3), NH(2), NO(2) and F groups in 3, 4, 5 and ipso carbonyl positions. Geometries of all derivatives were analyzed and it is ascertained that substitution has not important consequences on furan ring geometry. Differences of energy between OO-cis and trans conformers and energy barriers between them are described and extreme cases are explained. Interesting features appear in the cases of -NH(2) and -NO(2) groups, and particularly when the 3 and ipso carbonyl positions are substituted. Variations in energy barriers are correlated with variations in C2-C6 distances for the transition states and planar forms. Substitution effect on Mülliken charges are analyzed and related with internal rotation energy barriers and differences between conformers.     

Ab initio potential energy surface and vibration–rotation energy levels of germanium dicarbide,GeC2

The accurate ground‐state potential energy surface of germanium dicarbide, GeC₂, has been determined from ab initio calculations using the coupled‐cluster approach. The core–electron correlation, higher‐order valence‐electron correlation, and scalar relativistic effects were taken into account. The potential energy surface of GeC₂ was shown to be extraordinarily flat near the T‐shaped equilibrium configuration. The potential energy barrier to the linear CCGe configuration was predicted to be 1218 cm⁻¹. The vibration–rotation energy levels of some GeC₂ isotopologues were calculated using a variational method. The vibrational bending mode ν₃ was found to be highly anharmonic, with the fundamental wavenumber being only 58 cm⁻¹. Vibrational progressions due to this mode were predicted for the , , and states of GeC₂. © 2018 Wiley Periodicals, Inc.     

Potential energy surface of the photolysis of isocyanic acid HNCO

The dissociation curves of the photolysis of the isocyanic acid HNCO→HN+CO corresponding to the ground state (S0), the first triplet excited state (TO and the first singlet excited state (S1) have been studied respectively at the UHF/6-311G** and CIS/6-311G** levels using ab initio method. The energy surface crossing points, S1/T1 T1/S0 and S1/S0, have been found and the characteristics of the energy minimum crossing point were given, based on which, the changes of the crossing points' geometries along the lower electronic energy surface and its end-result have been located according to the steepest descent principle. The computational result indicates thatthe photolysis of the isocyanic acid HNCO→HN + CO has three competitive reaction channels ((A)-(C)), and from the kinetic piont of view, channel (A) is the most advantageous.     

Density functional calculation of conformations and potentials of internal rotation in polychlorinated biphenyls

Full geometry optimization for all 209 isomers of polychlorinated biphenyls (PCBs) and calculations of internal rotation potentials for 154 isomers have been performed by density functional method B3LYP/6-31G(d, p). Conformations and internal rotation barriers in PCBs were proved to depend on a number of chlorine atoms in ortho-positions and, less, the presence of chlorine atoms in adjacent meta-positions. Subject to the number of chlorine atoms in ortho-and adjacent meta-positions, 209 PCB isomers were classified into 18 groups, within each of them molecules having very close conformations and potentials of internal rotation. It makes possible to evaluate with high accuracy the potential functions of the last 55 PCB molecules for which potential curve calculations have not been made.