Calculating energy levels of isomerizing tetra-atomic molecules. II. The vibrational states of acetylene and vinylidene

A general, full-dimensional computational method for the accurate calculation of rotationally and vibrationally excited states of tetra-atomic molecules is further developed. The resulting computer program may be run in serial and parallel modes and is particularly appropriate for molecules executing wide-amplitude motions and isomerizations. An application to the isomerizing acetylene/vinylidene system is presented. Large-scale calculations using a coordinate system based on orthogonal satellite vectors have been performed in six dimensions and vibrational term values and wave functions for acetylene and vinylidene states up to approximately 23 000 cm(-1) above the potential minimum have been determined. This has permitted the characterization of acetylene and vinylidene states at and above the isomerization barrier. These calculations employ more extensive vibrational basis sets and hence consider a much higher density of states than in any variational calculations reported hitherto for this system. Comparison of the calculated density of states with that determined empirically suggests that our calculations are the most realistic achieved for this system to date. Indeed more states have been converged than in any previous study of this system. Calculations on lower lying excited states of acetylene based on HC-CH diatom-diatom coordinates give nearly identical results to those based on orthogonal satellite vectors. Comparisons are also made with calculations based on HH-CC diatom-diatom coordinates.     

Theoretical study of mechanism of cycloaddition reaction between dichloro‐germylene carbene (Cl2GeC:) and aldehyde

The mechanism of the cycloaddition reaction between singlet dichloro‐germylene carbene and aldehyde has been investigated with MP2/6‐31G* method, including geometry optimization and vibrational analysis for the involved stationary points on the potential energy surface. The energies of the different conformations are calculated by zero‐point energy and CCSD (T)//MP2/6‐31G* method. From the potential energy profile, it can be predicted that the reaction has two competitive dominant reaction pathways. The channel (A) consists of four steps: (1) the two reactants (R1, R2) first form an intermediate INT2 through a barrier‐free exothermic reaction of 142.4 kJ/mol; (2) INT2 then isomerizes to a four‐membered ring compound P2 via a transition state TS2 with energy barrier of 8.4 kJ/mol; (3) P2 further reacts with aldehyde (R2) to form an intermediate INT3, which is also a barrier‐free exothermic reaction of 9.2 kJ/mol; (4) INT3 isomerizes to a germanic bis‐heterocyclic product P3 via a transition state TS3 with energy barrier of 4.5 kJ/mol. The process of channel (B) is as follows: (1) the two reactants (R1, R2) first form an intermediate INT4 through a barrier‐free exothermic reaction of 251.5 kJ/mol; (2) INT4 further reacts with aldehyde (R2) to form an intermediate INT5, which is also a barrier‐free exothermic reaction of 173.5 kJ/mol; (3) INT5 then isomerizes to a germanic bis‐heterocyclic product P5 via a transition state TS5 with an energy barrier of 69.4 kJ/mol. © 2010 Wiley Periodicals, Inc. Int J Quantum Chem, 2011     

Ab initio Study of Mechanism of Forming Germanic Hetero-Polycyclic Compound between Germylene Carbene (H2Ge=C: ) and Formaldehyde

The mechanism of the cycloaddition reaction of forming germanic hetero‐polycyclic compound between singlet germylene carbene and formaldehyde has been investigated with MP2/6‐31G* method, including geometry optimization and vibrational analysis for the involved stationary points on the potential energy surface. The energies of the different conformations are calculated by CCSD (T)//MP2/6‐31G* method. From the potential energy profile, we predict that the cycloaddition reaction of forming germanic hetero‐polycyclic compound between singlet germylene carbene and formaldehyde has two competitive dominant reaction pathways. First dominant reaction pathway consists of four steps: (1) the two reactants (R1, R2) first form an intermediate (INT1) through a barrier‐free exothermic reaction of 117.5 kJ/mol; (2) intermediate (INT1) then isomerizes to a four‐membered ring compound (P2) via a transition state (TS2) with an energy barrier of 25.4 kJ/mol; (3) four‐membered ring compound (P2) further reacts with formaldehyde (R2) to form an intermediate (INT3), which is also a barrier‐free exothermic reaction of 19.6 kJ/mol; (4) intermediate (INT3) isomerizes to a germanic bis‐heterocyclic product (P3) via a transition state (TS3) with an energy barrier of 5.8 kJ/mol. Second dominant reaction pathway is as follows: (1) the two reactants (R1, R2) first form an intermediate (INT4) through a barrier‐free exothermic reaction of 197.3 kJ/mol; (2) intermediate (INT4) further reacts with formaldehyde (R2) to form an intermediate (INT5), which is also a barrier‐free exothermic reaction of 141.3 kJ/mol; (3) intermediate (INT5) then isomerizes to a germanic bis‐heterocyclic product (P5) via a transition state (TS5) with an energy barrier of 36.7 kJ/mol.     

Theoretical study of mechanism of cycloaddition reaction between singlet dichlorosilylene carbene (Cl<Subscript>2</Subscript>Si=C:) and formaldehyde

The mechanism of the cycloaddition reaction between singlet dichlorosilylene carbene (Cl₂Si=C:) and formaldehyde has been investigated with MP2/6-31G* method, including geometry optimization and vibrational analysis for the involved stationary points on the potential energy surface. The energies of the different conformations are calculated by Zero-point energy and CCSD (T)//MP2/6-31G* method. From the potential energy profile, it can be predicted that the reaction has two competitive dominant reaction pathways. The first dominant reaction pathway consists of two steps: (1) the two reactants (R1, R2) firstly form a four-membered ring intermediate (INT4) through a barrier-free exothermic reaction of 387.9 kJ/mol; (2) intermediate (INT4) then isomerizes to H-transfer product (P4.2) via a transition state (TS4.2) with energy barrier of 4.7 kJ/mol. The second dominant reaction pathway as follows: on the basis of intermediate (INT4) created between R1 and R2, intermediate (INT4) further reacts with formaldehyde (R2) to form the intermediate (INT5) through a barrier-free exothermic reaction of 158.3 kJ/mol. Then, intermediate (INT5) isomerizes to a silicic bis-heterocyclic product (P5) via a transition state (TS5), for which the barrier is 40.1 kJ/mol.     

Short-time Fourier transform analysis of ab initio molecular dynamics simulation: collision reaction between CN and C4H6

Collision reactions between cyano radical (CN) and dimethylacetylene (C4H6) are thought to occur in the atmosphere of Saturn's moon Titan. However, it is difficult to reproduce reactions occurring in unique environments to study their dynamical processes. In this study, collision reactions between CN and C4H6 were investigated using ab initio molecular dynamics (AIMD) simulations. The simulation results were categorized into three kinds: nonreactive collision, incorporation, and substitution. Short-time Fourier transform analysis of velocity autocorrelation functions obtained by the AIMD simulations, which has been recently developed by our research group, was performed to examine the nonequilibrium condition of the vibrational states. Spectrograms, which correspond to the time evolution of power spectra, clarify the relationship between the three reaction channels and the dynamical changes of the vibrational states.     

Ab initio rate constants from hyperspherical quantum scattering: application to H+C2H6 and H+CH3OH

The dynamics and kinetics of the abstraction reactions of H atoms with ethane and methanol have been studied using a quantum mechanical procedure. Bonds being broken and formed are treated with explicit hyperspherical quantum dynamics. The ab initio potential energy surfaces for these reactions have been developed from a minimal number of grid points (average of 48 points) and are given by analytical functionals. All the degrees of freedom except the breaking and forming bonds are optimized using the second order perturbation theory method with a correlation consistent polarized valence triple zeta basis set. Single point energies are calculated on the optimized geometries with the coupled cluster theory and the same basis set. The reaction of H with C2H6 is endothermic by 1.5 kcal/mol and has a vibrationally adiabatic barrier of 12 kcal/mol. The reaction of H with CH3OH presents two reactive channels: the methoxy and the hydroxymethyl channels. The former is endothermic by 0.24 kcal/mol and has a vibrationally adiabatic barrier of 13.29 kcal/mol, the latter reaction is exothermic by 7.87 kcal/mol and has a vibrationally adiabatic barrier of 8.56 kcal/mol. We report state-to-state and state-selected cross sections together with state-to-state rate constants for the title reactions. Thermal rate constants for these reactions exhibit large quantum tunneling effects when compared to conventional transition state theory results. For H+CH3OH, it is found that the CH2OH product is the dominant channel, and that the CH3O channel contributes just 2% at 500 K. For both reactions, rate constants are in good agreement with some measurements.     

Reduced dimension discrete variable representation study of cis-trans isomerization in the S1 state of C2H2

Isomerization between the cis and trans conformers of the S(1) state of acetylene is studied using a reduced dimension discrete variable representation (DVR) calculation. Existing DVR techniques are combined with a high accuracy potential energy surface and a kinetic energy operator derived from FG theory to yield an effective but simple Hamiltonian for treating large amplitude motions. The spectroscopic signatures of the S(1) isomerization are discussed, with emphasis on the vibrational aspects. The presence of a low barrier to isomerization causes distortion of the trans vibrational level structure and the appearance of nominally electronically forbidden A? (1)A(2)←X? (1)Σ(g)(+) transitions to vibrational levels of the cis conformer. Both of these effects are modeled in agreement with experimental results, and the underlying mechanisms of tunneling and state mixing are elucidated by use of the calculated vibrational wavefunctions.     

Theoretical study of mechanism of forming a silapolycyclic compound between methylenesilylene and acetone

The mechanism of the cycloaddition reaction of forming a silapolycyclic compound between singlet methylenesilylene and acetone has been investigated with MP2/6‐31G* method, including geometry optimization and vibrational analysis for the involved stationary points on the potential energy surface. The energies of the different conformations are calculated by CCSD(T)//MP2/6‐31G* method. From the potential energy profile, we predict that the cycloaddition reaction of forming a silapolycyclic compound between singlet methylenesilylene and acetone has two competitive dominant reaction pathways. First dominant reaction pathway consists of four steps: (I) the two reactants (R1, R2) first form an intermediate (INT1) through a barrier‐free exothermic reaction of 46.2 kJ/mol; (II) intermediate (INT1) then isomerizes to a planar four‐membered ring product (P3) via transition state (TS3) with an energy barrier of 47.1 kJ/mol; (III) planar four‐membered ring product (P3) further reacts with acetone (R2) to form an intermediate (INT4), which is also a barrier‐free exothermic reaction of 40.0 kJ/mol; (IV) intermediate (INT4) isomerizes to a silapolycyclic compound (P4) via transition state (TS4) with an energy barrier of 57.0 kJ/mol. Second dominant reaction pathway consists of three steps: (I) the two reactants (R1, R2) first form a four‐membered ring intermediate (INT2) through a barrier‐free exothermic reaction of 0.5 kJ/mol; (II) INT2 further reacts with acetone (R2) to form an intermediate (INT5), which is also a barrier‐free exothermic reaction of 45.4 kJ/mol; (III) intermediate (INT5) isomerizes to a silapolycyclic compound (P5) via transition state (TS5) with an energy barrier of 49.3 kJ/mol. P4 and P5 are isomeric compounds. © 2009 Wiley Periodicals, Inc. Int J Quantum Chem, 2010     

Ultrafast dynamics of the azobenzene-coumarin complex: investigation of cooling dynamics measured by an integrated molecular thermometer

The energy dissipation mechanism from photoexcited azobenzene (Az) was studied by femtosecond time-resolved UV absorption spectroscopy using 7-amino-4-trifluoromethylcoumarin (ATC) as a probe. The distance between the probe molecule and Az was fixed by covalently linking them together through a rigid proline spacer. Picosecond dynamics in THF solutions were studied upon excitation into the S1 state by a 100 fs laser pulse at 480 nm. Transient absorption spectra obtained for Az-Pro-ATC combined the S1 state absorption and vibrationally excited ground-state absorption of ATC. Correction of the transient spectrum of Az-Pro-ATC for the S1 absorption provided the time-resolved absorption spectrum of the ATC hot band. Three major components were observed in the transient kinetics of Az-Pro-ATC vibrational cooling. It is proposed that in ca. 0.25 ps after the excitation, the S1 state of azobenzene decays to form an initial vibrationally excited nonthermalized ground state of Az-Pro-ATC that involves vibrational modes of both azobenzene and coumarin. This hot ground state decays in ca. 0.32 ps to the next, vibrationally equilibrated, transient state by redistributing the energy within the molecule. Subsequently, the latter state cools by transferring its energy to the closest solvent molecules in ca. 5 ps; then, the energy diffuses to the bulk solvent in 13 ps.     

二硅烯异构化反应的理论研究, 从头等水平上的动力学, 热力学分析

本文在从头算水平上计算了二硅烯HXSi-SiH2(X=H,D)异构化反应的反应物、产物及过渡态构型的能量、谐振动频率和反应活化能等,又计算了反应的热力学函数变化, 平衡常数及速率常数, 结果表明,该异构化反应是放热的, 且可自发进行, 结论与Newman的实验事实相符合, 值得注意的是, 零点能校正对该异构化反应的计算有改进。     

Theoretical study on the mechanism of cycloaddition reaction between dimethyl germylidene and formaldehyde

The cycloaddition mechanism of the reaction between singlet dimethyl germylidene and formaldehyde has been investigated with MP2/6-31G* method, including geometry optimization and vibrational analysis for the involved stationary points on the potential energy surface. The energies of the different conformations are calculated with CCSD (T)//MP2/6-31G* method. From the potential energy profile, we predict that the cycloaddition reaction between singlet dimethyl germylidene and formaldehyde has two dominant reaction pathways. First dominant reaction pathway consists of three steps: (1) the two reactants (R1, R2) firstly form an intermediate INT1a through a barrier-free exothermic reaction of 43.0 kJ/mol; (2) INT1a then isomerizes to a four-membered ring compound P1 via a transition state TS1a with an energy barrier of 24.5 kJ/mol; (3) P1 further reacts with formaldehyde(R2) to form a germanic heterocyclic compound INT3, which is also a barrier-free exothermic reaction of 52.7 kJ/mol; Second dominant reaction pathway is as following: (1) the two reactants (R1, R2) firstly form a planar four-membered ring intermediate INT1b through a barrier-free exothermic reaction of 50.8 kJ/mol; (2) INT1b then isomerizes to a twist four-membered ring intermediate INT1.1b via a transition state TS1b with an energy barrier of 4.3 kJ/mol; (3) INT1.1b further reacts with formaldehyde(R2) to form an intermediate INT4, which is also a barrier-free exothermic reaction of 46.9 kJ/mol; (4) INT4 isomerizes to a germanic bis-heterocyclic product P4 via a transition state TS4 with an energy barrier of 54.1 kJ/mol.     

An ab initio molecular orbital study of the C2F2 species: The difluorovinylidene → difluoroacetylene rearrangement

An ab initio MO study, using medium size Gaussian basis sets has been made of vinylidene carbene, acetylene and the isomeric cyclic intermediate presumed to represent the transition state of their interconversion reaction, along with their perfluorinated analogs. The total energies of the acetylenes are lower than the vinylidenes and the estimated activation energy of their interconversion is considerably higher for the fluorinated molecules. The results are in line with experimental observations.     

Vibrational Relaxation in beta-Carotene Probed by Picosecond Stokes and Anti-Stokes Resonance Raman Spectroscopy

Picosecond time-resolved Stokes and anti-Stokes resonance Raman spectra of all-trans-beta-carotene are obtained and analyzed to reveal the dynamics of excited-state (S(1)) population and decay, as well as ground-state vibrational relaxation. Time-resolved Stokes spectra show that the ground state recovers with a 12.6 ps time constant, in agreement with the observed decay of the unique S(1) Stokes bands. The anti-Stokes spectra exhibit no peaks attributable to the S(1) (2A(g) (-)) state, indicating that vibrational relaxation in S(1) must be nearly complete within 2 ps. After photoexcitation there is a large increase in anti-Stokes scattering from ground-state modes that are vibrationally excited through internal conversion. The anti-Stokes data are fit to a kinetic scheme in which the C=C mode relaxes in 0.7 ps, the C-C mode relaxes in 5.4 ps and the C-CH(3) mode relaxes in 12.1 ps. These results are consistent with a model for S(1)-S(0) internal conversion in which the C=C mode is the primary acceptor, the C-C mode is a minor acceptor, and the C-CH(3) mode is excited via intramolecular vibrational energy redistribution.     

Theoretical study of isomerization and dissociation of acetylene dication in the ground and excited electronic states

Ab initio calculations employing the configuration interaction method including Davidson's corrections for quadruple excitations have been carried out to unravel the dissociation mechanism of acetylene dication in various electronic states and to elucidate ultrafast acetylene-vinylidene isomerization recently observed experimentally. Both in the ground triplet and the lowest singlet electronic states of C2H2(2+) the proton migration barrier is shown to remain high, in the range of 50 kcal/mol. On the other hand, the barrier in the excited 2 3A" and 1 3A' states decreases to about 15 and 34 kcal/mol, respectively, indicating that the ultrafast proton migration is possible in these states, especially, in 2 3A", even at relatively low available vibrational energies. Rice-Ramsperger-Kassel-Marcus calculations of individual reaction-rate constants and product branching ratios indicate that if C2H(2)2+ dissociates from the ground triplet state, the major reaction products should be CCH+(3Sigma-)+H+ followed by CH+(3Pi)+CH+(1Sigma+) and with a minor contribution (approximately 1%) of C2H+(2A1)+C+(2P). In the lowest singlet state, C2H+(2A1)+C+(2P) are the major dissociation products at low available energies when the other channels are closed, whereas at Eint>5 eV, the CCH+(1A')+H+ products have the largest branching ratio, up to 70% and higher, that of CH+(1Sigma+)+CH+(1Sigma+) is in the range of 25%-27%, and the yield of C2H++C+ is only 2%-3%. The calculated product branching ratios at Eint approximately 17 eV are in qualitative agreement with the available experimental data. The appearance thresholds calculated for the CCH++H+, CH++CH+, and C2H++C+ products are 34.25, 35.12, and 34.55 eV. The results of calculations in the presence of strong electric field show that the field can make the vinylidene isomer unstable and the proton elimination spontaneous, but is unlikely to significantly reduce the barrier for the acetylene-vinylidene isomerization and to render the acetylene configuration unstable or metastable with respect to proton migration.     

Dynamical properties of hydrogen sulphide motion in its clathrate hydrate from ab initio and classical isobaric-isothermal molecular dynamics

Equilibrium ab initio (AI) and classical constant pressure-constant temperature molecular dynamics (MD) simulations have been performed to investigate the dynamical properties in (type I) hydrogen sulphide hydrate at 150 and 300 K and 1 bar, and also lower temperatures, with particular scrutiny of guest motion. The rattling motions of the guests in the large and small cavities were around 45 and 75-80 cm(-1), respectively, from AIMD, with the corresponding classical MD modes being 10-12 cm(-1) less at 150 K and around 5 cm(-1) lower at 300 K. The rattling motion in the small cavity overlapped somewhat with the translational motion of the host lattice (with modes at circa 85 and 110 cm(-1)), due in part to a smaller cage radius and more frequent occurrences of guest-host hydrogen bonding leading to greater coupling in the motion. The experimentally determined H-S stretch and H-S-H bending frequencies, in the vicinity of 2550-2620 and 1175 cm(-1) [H.R. Richardson et al., J. Chem. Phys.1985, 83, 4387] were reproduced successfully in the AIMD simulations. Consideration of Kubic harmonics for the guest molecules from AIMD revealed that a preferred orientation of the dipole-vector (or C(2)-axis) exists at 150 K vis--vis the [100] cube axis in both the small and large cavities, but is markedly more significant for the small cavity, while there is no preferred orientation at 300 K. In comparison, classical MD did not reveal any preferred orientation at either temperature, or at 75 K (closer to the AIMD simulation at 150 K vis-à-vis that approach's estimated melting point). Probing rotational dynamics of the guests reinforced this temperature effect, revealing more rapid rotational time scales at 300 K with faster decay times of dipole-vector (C(2)) and H-H-vector (C(2)(y)) being similar for each cage, at around 0.25 and 0.2 ps, respectively, versus approximately 0.45 and 0.5 ps (large) and 0.8 ps (small) at 150 K. It was found that the origin of the observed preferred orientations, especially in the small cages, at 150 K via AIMD was attributable to optimization of the dipolar interaction between the guest and outward-pointing water dipoles in the cavity, with guests "flitting" rotationally between various such configurations, forming occasionally hydrogen bonds with the host molecules.     

The vinylidene-acetylene isomerization barrier

The barrier to rearrangement of vinylidene to acetylene has been determined using Møller-Plesset perturbation theory and an extended polarized basis set. With the inclusion of zero-point vibrational corrections, the barrier is found to be only 0.9 $\text{kcal}\text{mole}$, suggesting that vinylidene will have an extremely short lifetime.     

Accurate partition function for acetylene, 12C2H2, and related thermodynamical quantities

The internal partition function (Q(int)) of ethyne (acetylene), (12)C(2)H(2), is calculated by explicit summation of the contribution of all individual vibration-rotation energy levels up to 15,000 cm(-1). The corresponding energies are predicted from a global model and constants reproducing within 3σ all 18,415 published vibration-rotation lines in the literature involving vibrational states up to 8900 cm(-1), as produced by Amyay et al. [J. Mol. Spectrosc. 267, 80 (2011)]. Values of Q(int), with distinct calculations for para and ortho species are provided from 1 to 2000 K, in step of 1 K. The total internal partition function at 298.15 K is 104.224387(47) or 416.89755(19), with the nuclear degeneracy spin factors taken as 1/4:3/4 (astronomer convention) or 1:3 (atmospheric convention), respectively, for para:ortho species. The Helmholtz function, Gibbs enthalpy function, entropy, and specific heat at constant pressure are also calculated over the same temperature range. Accuracies as well as the missing contribution of the vinylidene isomer of acetylene in the calculations are discussed.     

Acetylene-vinylidene isomerization in ultrashort intense laser fields studied by triple ion-coincidence momentum imaging

The isomerization of acetylene via hydrogen migration in intense laser fields (8 x 10(14) W/cm2) has been investigated by coincidence momentum imaging of the three-body Coulomb explosion process, C2H2 (3+)-->H+ + C+ + CH+. When ultrashort (9 fs) laser pulses are used, the angle between the momenta of C+ and H+ fragments exhibits a sharp distribution peaked at a small angle ( approximately 20 degrees ), showing that the hydrogen atom remains near the original carbon site in the acetylene configuration. On the other hand, a significantly broad distribution extending to larger momentum angles ( approximately 120 degrees ) is observed when the pulse duration is increased to 35 fs, indicating that the ultrafast isomerization to vinylidene is induced in the longer laser pulse.     

Theoretical study of mechanism of cycloaddition reaction between dimethylmethylenesilylene and formaldehyde

The mechanism of cycloaddition reaction between singlet dimethylmethylenesilylene and formaldehyde has been investigated with MP2/6‐31G* method, including geometry optimization and vibrational analysis for the involved stationary points on the potential energy surface. The energies of different conformations are calculated by CCSD(T)//MP2/6‐31G* method. From the potential energy surface, it can be considered in thermodynamics and dynamics that reaction (1) and reaction (4) are the two dominant competitive reaction channels of cycloaddition reaction between dimethylmethylenesilylene and formaldehyde. The reaction process of reaction (1) is that: the two reactants (R1, R2) first form intermediates INT1a and INT1b through two reaction paths, a and b, which are barrier‐free exothermic reactions of 31.8 and 43.9 kJ/mol; then, INT1a and INT1b isomerize to a four‐membered ring product P1 via transition states TS1a and TS1b, with energy barriers of 26.3 and 24.4 kJ/mol. Reaction (4) also has two reaction paths, a and b, each of which consists of three steps are as follows: (i) the two reactants (R1, R2) first form intermediates INT3a and INT3b, which are barrier‐free exothermic reactions of 64.5 and 44.2 kJ/mol. (ii) INT3a and INT3b further react with formaldehyde (R2) to form intermediates INT4a and INT4b, through barrier‐free exothermic reactions of 22.9 and 22.2 kJ/mol. (iii) INT4a and INT4b then isomerize to form silapolycyclic product P4 via transition states TS4a and TS4b, with energy barriers of 39.7 and 29.3 kJ/mol. © 2008 Wiley Periodicals, Inc. Int J Quantum Chem, 2008