High‐precision Hy–CI variational calculations for the ground state of neutral helium and helium‐like ions

Hylleraas–configuration interaction (Hy–CI) method variational calculations with up to 4648 expansion terms are reported for the ground ¹S state of neutral helium. Convergence arguments are presented to obtain estimates for the exact nonrelativistic energy of this state. The nonrelativistic energy is calculated to be ?2.9037 2437 7034 1195 9829 99 a.u. Comparisons with other calculations and an energy extrapolation give an estimated nonrelativistic energy of ?2.9037 2437 7034 1195 9830(2) a.u., which agrees well with the best previous variational energy, ?2.9037 2437 7034 1195 9829 55 a.u., of Korobov (Phys Rev A 2000, 61, 64503), obtained using the universal (exponential) variational expansion method with complex exponents (Frolov, A. M.; Smith, V. H. Jr. J Phys B Atom Mol Opt Phys 1995, 28, L449). In addition to He, results are also included for the ground ¹S states of H^?, Li⁺, Be⁺⁺, and B⁺³. © 2002 Wiley Periodicals, Inc. Int J Quantum Chem, 2002     

The effect of confinement on the electronic energy and polarizability of a hydrogen molecular ion

The electronic energy and the polarizability of a confined hydrogen molecular ion in the ground state and the first excited state, for cavities of different volumes, are calculated using the variational method. In the treatment adopted an alternative molecular wave function is introduced with only one variational parameter and based on wave functions used for confined atoms. © 2016 Wiley Periodicals, Inc.     

Direct dynamics studies on the hydrogen abstraction reactions CF3O+CH4(CD4)→CF3OH(CF3OD)+CH3(CD3)

The dynamics properties of the hydrogen abstraction reaction CF₃O+CH₄→CF₃OH+CH₃ are studied by dual-level direct dynamics method. Optimization calculations are preformed by B3LYP and MP2 with the 6-311G(d,p) basis set, and the single-point calculations are done at the multi-coefficient correction method based on quadratic configuration interaction with single and double excitations (MC-QCISD) method. The rate constants are evaluated by canonical variational transition-state theory with a small-curvature tunneling correction over a wide range of temperature 200–2000 K. The agreement between theoretical and experimental rate constants is good in the measured temperature range. The calculated results show that the variational effect is small and almost neglected over the whole temperature range, whereas, the tunneling correction plays a role in the lower temperature range. The kinetic isotope effect for the reaction is ‘normal’. The value of k_H/k_D is 2.38 at room temperature and it decreases with the temperature increasing.     

Electronic quantum Monte Carlo calculations of atomic forces, vibrations, and anharmonicities

Atomic forces are calculated for first-row monohydrides and carbon monoxide within electronic quantum Monte Carlo (QMC). Accurate and efficient forces are achieved by using an improved method for moving variational parameters in variational QMC. Newton's method with singular value decomposition (SVD) is combined with steepest-descent (SD) updates along directions rejected by the SVD, after initial SD steps. Dissociation energies in variational and diffusion QMC agree well with the experiment. The atomic forces agree quantitatively with potential-energy surfaces, demonstrating the accuracy of this force procedure. The harmonic vibrational frequencies and anharmonicity constants, derived from the QMC energies and atomic forces, also agree well with the experimental values.     

Molecular dynamics,root-mean-square amplitudes,statistical thermodynamics,and molecular polarizability for the isotopic species of dioxygen monofluoride

A brief survey of vibrational spectral studies for the four isotopic species of dioxygen monofluoride has been made. On the basis of group theoretical considerations, symmetry coordinates have been constructed and kinetic energy matrices (orG matrix elements), potential energy matrices, and secular equations have been derived to calculate the valence force constants. The mean-square amplitudes and root-mean-square amplitudes for both the bonded and nonbonded atom pairs have been calculated at the room temperature. On the basis of a rigid rotator and harmonic oscillator model, enthalpy function, free enthalpy function, entropy, and heat capacity have been calculated from 200 to 2000 °K for all the four isotopic species. On the basis of a delta-function potential model based on the variational method and delta-function electronic wave functions, the bond parallel components, the bond perpendicular components, the contribution by the nonbonding electrons, and the average molecular polarizability have been calculated. The results obtained from these studies clearly confirm a double bond character for the oxygen—oxygen distance and a bond order of less than one-half for the oxygen—fluorine distance. The results have been discussed in relation to the nature of the two characteristic bonds involved in this molecular system.     

Direct dynamics study of the hydrogen abstraction reaction of CF3CH2Cl + Cl → CF3CHCl + HCl

The hydrogen abstraction reaction of Cl atoms with CF₃CH₂Cl (HCFC‐133a) is investigated by using density function theory and ab initio approach, and the rate constants are calculated by using the dual‐level direct dynamics method. Optimized geometries and frequencies of reactants, transition state, and products are computed at the B3LYP/6‐311+G(2d,2p) level. To refine the energetic information along the minimum energy path, single‐point energy calculations are carried out at the G3(MP2) level of theory. The interpolated single‐point energy method is employed to correct the energy profiles for the title reaction. The rate constants are evaluated by using the canonical variational transition state theory with a small‐curvature tunneling correction over a wide range of temperature, 200–2000 K. The variational effect for the reaction is moderate at low temperatures and very small at high temperatures. However, the tunneling correction has an important contribution in the lower temperature range. The agreement between calculated rate constants and available experimental values is good at lower temperatures but diverges significantly at higher temperatures. © 2012 Wiley Periodicals, Inc. Int J Chem Kinet 44: 661–667, 2012     

An analytic hindered rotor model for calculating microcanonical variational unimolecular rate constants from reaction path properties

A model is proposed for performing microcanonical variational transition state theory calculations which incorporates ideas from vibrator and flexible variational transition state models. Vibrational frequencies, moments of inertia, and potential energy for the variational transition state are found by reaction path following as for the vibrator model. However, the transitional modes are treated as hindered rotors using an analytic potential and an analytic density of states, which are fit to barriers for hindered rotation determined from reaction path following. The model proposed here differs from the flexible transition state model in that the density of states for the transitional modes is analytic and transitional modes and external rotational angular momenta are uncoupled. For the H + CH₃ ? CH₄ system, rate constants calculated with this new model are only 6–23% smaller on average from those of the flexible transition state model for values of total angular momentum which correspond to average rotational temperatures of 0–2000 K. Harmonic frequencies calculated for the transitional modes from the hindered rotor Hamiltonian are in good agreement with the exact values found by a reaction path analysis. © 1994 John Wiley & Sons, Inc.     

Multi-component molecular orbital study of isotope effects on lithium hydride molecules with the configuration interaction scheme

The multi-component molecular orbital method, which can take account of the quantum effect of the electrons and nuclei, is applied to the calculation of lithium hydride isotope species with the configuration interaction (CI) scheme. The optimum basis set functions for quantum nuclei are proposed by the fully variational procedure under single electronic–single nuclear excitation CI level. The average internuclear distances and dipole moments for isotopic lithium hydride molecules calculated with small basis functions are reasonable agreement with the corresponding experimental values.     

Multiconfigurational expansions of density operators: equations of motion and their properties

 Multiconfigurational expansions of density operators which may be used in numerical treatments of the dynamics of closed and open quantum systems are introduced. The expansions of the density operators may be viewed as analogues of those used in the multiconfiguration time-dependent Hartree (MCTDH) method, which is a well-established and highly efficient method for propagating wavepackets in several dimensions. There is no unique multiconfigurational representation of a density operator and two sensible types of MCTDH-like expansions are studied. Equations of motion for these multiconfigurational expansions are presented by adopting the Dirac–Frenkel/McLachlan variational principle (or variants of thereof). Various properties of these sets of equations of motion are derived for closed and open system dynamics. The numerical and technical aspects of this approach have been recently discussed by us [(1999) J Chem Phys 111: 8759]. Here we discuss the formal aspects of the approach in a more general context. Received: 26 January 2000 / Accepted: 8 February 2000 / Published online: 12 May 2000     

Mechanistic study and kinetic properties of the CF3CHO + Cl reaction

Theoretical investigations have been carried out on the mechanism and kinetics for the reaction of CF 3 CHO + Cl using duallevel direct dynamics method. The potential energy surface information was obtained at the MCQCISD/3//MP2/cc-pVDZ level and the kinetic calculations were done using variational transition state theory with interpolated single-point energy (VTST-ISPE) approach. The calculated results show that the reaction proceeds primarily via the H-abstraction channel, while the Cl-addition channel is unfavorable due to the higher barriers. The improved canonical variational transition-state theory (ICVT) with the small-curvature tunneling correction (SCT) was used to calculate the rate constants. The theoretical rate constants at room temperature are in general agreement with the experimental values. A three-parameter rate constant expression was fitted over a wide temperature range of 200-2000 K.     

Direct ab initio dynamics studies on the hydrogen-abstraction reactions of OH radicals with HOX (X = F, Cl, and Br)

The hydrogen abstract reactions of OH radicals with HOF (R1), HOCl (R2), and HOBr (R3) have been studied systematically by a dual-level direct-dynamics method. The geometries and frequencies of all the stationary points are optimized at the MP2/6-311+G(2d, 2p) level of theory. A hydrogen-bonded complex is located at the product channel for the OH + HOBr reaction. To improve the energetics information along the minimum energy path (MEP), single-point energy calculations are carried out at the CCSD(T)/6-311++G(3df, 3pd) level of theory. Interpolated single-point energy (ISPE) method is employed to correct the energy profiles for the three reactions. It is found that neither the barrier heights (DeltaE) nor the H-O bond dissociation energies [D(H-O)] exhibit any clear-cut linear correlations with the halogen electronegative. The decrease of DeltaE and D(H-O) for the three reactions are in order of HOF > HOBr > HOCl. Rate constants for each reaction are calculated by canonical variational transition-state theory (CVT) with a small-curvature tunneling correction (SCT) within 200-2000 K. The agreement of the rate constants with available experimental values for reactions R2 and R3 at 298 K is good. Our results show that the variational effect is small while the tunneling correction has an important contribution in the calculation of rate constants in the low-temperature range. Due to the lack of the kinetic data of these reactions, the present theoretical results are expected to be useful and reasonable to estimate the dynamical properties of these reactions over a wide temperature range where no experimental value is available.     

On the kinetic mechanism of the hydrogen abstraction reactions of the hydroxyl radical with CH3CF2Cl and CH3CFCl2: A dual level direct dynamics study

By means of the dual‐level direct dynamics method, the mechanisms of the reactions, CH₃CF₂Cl + OH → products (R1) and CH₃CFCl₂ + OH → products (R2), are studied over a wide temperature range 200–2000 K. The optimized geometries and frequencies of the stationary points are calculated at the MP2/6‐311G(d,p) level, and then the energy profiles of the reactions are refined with the interpolated single‐point energy method at the G3(MP2) level. The canonical variational transition‐state theory with the small‐curvature tunneling (SCT) correction method is used to calculate the rate constants. For the title reactions, three reaction channels are identified and the H‐abstraction channel is the major pathway. The results indicate that F substitution has a significant (reductive) effect on hydrochlorofluorocarbon reactivity. Also, for all H‐abstraction reaction channels the variational effect is small and the SCT effect is only important in the lower temperature range on the rate constants calculation. © 2009 Wiley Periodicals, Inc. J Comput Chem, 2010     

Hydrogen abstraction reactions of OH radicals with CH₃CH₂CH₂Cl and CH₃CHClCH₃: a mechanistic and kinetic study

The hydrogen abstraction reactions of OH radicals with CH₃CH₂CH₂Cl (R1) and CH₃CHClCH₃ (R2) have been investigated theoretically by a dual‐level direct dynamics method. The optimized geometries and frequencies of the stationary points are calculated at the B3LYP/6‐311G(d,p) level. To improve the reaction enthalpy and potential barrier of each reaction channel, the single point energy calculation is performed by the BMC‐CCSD method. Using canonical variational transition‐state theory (CVT) with the small‐curvature tunneling correction, the rate constants are evaluated over a wide temperature range of 200–2000 K at the BMC‐CCSD//B3LYP/6‐311G(d,p) level. For the reaction channels with the negative barrier heights, the rate constants are calculated by using the CVT. The calculated total rate constants are consistent with available experimental data. The results show that at lower temperatures, the tunneling correction has an important contribution in the calculation of rate constants for all the reaction channels with the positive barrier heights, while the variational effect is found negligible for some reaction channels. For reactions OH radicals with CH₃CH₂CH₂Cl (R1) and CH₃CHClCH₃ (R2), the channels of H‐abstraction from –CH₂– and –CHCl groups are the major reaction channels, respectively, at lower temperatures. With temperature increasing, contributions from other channels should be taken into account. Finally, the total rate constants are fitted by two models, i.e., three‐parameter and four‐parameter expressions. The enthalpies of formation of the species CH₃CHClCH₂, CH₃CHCH₂Cl, and CH₂CH₂CH₂Cl are evaluated by isodesmic reactions. © 2011 Wiley Periodicals, Inc. J Comput Chem, 2011     

DFT approach to calculate electronic transfer through a segment of DNA double helix

The electronic structures of an entire segment of a DNA molecule were calculated in its single‐strand and double‐helix cases using the DFT method with an overlapping dimer approximation and negative factor counting method. The hopping conductivity of the segment was calculated by the random walk theory from the results of energy levels and wave functions obtained. The results of the single‐strand case show that the DFT method is quantitatively in agreement with that of the HF MP2 method. The results for the double helix are in good agreement with that of the experimental data. Therefore, the long‐range electron transfer through the DNA molecule should be caused by hopping of electronic charge carriers among different energy levels whose corresponding wave functions are localized at different bases of the DNA molecule. © 2000 John Wiley & Sons, Inc. J Comput Chem 21: 1109–1117, 2000     

Direct dynamics studies for the reactions of CF3CHFCF3 and CF3CF2CHF2 with H atoms

The rate constants of the hydrogen abstraction reactions of CF₃CHFCF₃ + H (R1) and CF₃CF₂CHF₂ + H (R2) have been calculated by means of the dual-level direct dynamics method. Optimized geometries and frequencies of stationary points and extra points along the minimum-energy path (MEP) are obtained at the MPW1K/6-311+G(d,p) level, and the classical energetic information is further corrected with the interpolated single-point energy (ISPE) approach by the G3(MP2) level of theory. Using the canonical variational transition state theory (CVT) with small-curvature tunneling corrections (SCT), the rate constants are evaluated over a wide temperature range of 200-2000 K. The calculated CVT/SCT rate constants are in good agreement with available experimental values. It is found that the variational effect is very small and almost negligible over the whole temperature region. However, the small-curvature tunneling correction plays an important role in the lower temperature range. Furthermore, the heats of formation of species CF₃CF₂CHF₂ (SC₁ or SC₂) and CF₃CF₂CF₂ are studied using isodesmic reactions to further elucidate the thermodynamic properties.     

Direct dynamic study on the hydrogen abstraction reaction of H2CO with NCO

A direct ab initio dynamics method is used to investigate the hydrogen‐abstraction reaction of H₂CO with NCO. The potential energy surface information is obtained at the MP2/6‐311G(d,p) level. More accurate single‐point energy is refined at the G3(MP2)//MP2/6‐311G(d,p) level. Furthermore, the rate constants of reaction H₂CO + NCO are evaluated by using the canonical variational transition state theory with small‐curvature tunneling contributions over a wide temperature range of 200–2000 K. The calculated reaction enthalpy and rate constants are in good agreement with the available experimental values. © 2009 Wiley Periodicals, Inc. Int J Chem Kinet 41: 394–400, 2009     

Spectroscopic calculation of the bond-dissociation energy of CH bonds in fluoro derivatives of methane,ethane, ethene,propene, and benzene

The bond-dissociation energy of CH bonds in fluoro derivatives of methane, ethane, ethene, propene, and benzene is determined by spectroscopic and quantum chemical methods. The spectroscopic values of the bond-dissociation energy of CH bonds are calculated in terms of fundamental absorption bands in the anharmonic approximation by the variational method using the Morse anharmonic basis. The quantum chemical calculations are performed using the 6-311G(3df, 3pd)/B3LYP basis set. The obtained regularities in variations of the CH bond dissociation energy values upon changes in the molecule structure are discussed.     

SCF DVM-Xα with basis set of numerical Hartree—Fock functions and its applications to MoF6, WF6, and UF6

A self-consistent version of the discrete variational method is described based on the use of numerical LCAO basis functions obtained as solutions of the Hartree—Fock equations for free atoms. Sets of single-zeta Slater functions are applied to approximate atomic densities further employed in the calculations of the Coulomb potential. The computer programs realizing this approach have been written and utilized to calculate electronic structures of molybdenum, tungsten and uranium hexafluorides. The ionization potentials calculated are in good quantitative agreement with experimental data. The deviations of the calculated valence state IP's from those determined by photoelectron spectroscopy do not exceed 1 eV.     

Reaction path dynamics and theoretical rate constants for the SiH3Cl+H→SiH2Cl+H2 reaction by ab initio direct dynamics method

Ab initio direct dynamics method has been used to study the title reaction. Electronic structure information including geometries, gradients and force constants (Hessians) are calculated at the UQCISD/6-311+G^** level. Energies along the minimum energy path are improved by a series of single-point G2//QCISD calculations. The changes of the geometries, vibratioanal frequencies, potential energies and total curvature along the reaction path are discussed. The rate constants in the temperature range 200–3000 K are calculated by canonical variational transition state theory with small-curvature tunneling correction (CVT/SCT) method. The results show that the variational effect is small and in the lower temperature range, the small curvature tunneling effect is important for the reaction.     

Dual-level direct dynamics studies for the reactions of OH radical with bromine-substituted ethanes

The dynamic properties of the multichannel hydrogen abstraction reactions of CH(3)CH(2)Br + OH --> products and CH(3)CHBr(2) + OH --> products are studied by dual-level direct dynamics method. For each reaction, three reaction channels, one for alpha-hydrogen abstraction and two for beta-hydrogen abstractions, have been identified. The minimum energy paths (MEPs) of both the reactions are calculated at the Becke's half-and-half (BH&H)-Lee-Yang-Parr (LYP)/6-311G(d, p) level and the energy profiles along the MEPs are further refined with interpolated single-point energies (ISPE) method at the G2M(RCC5)//BH&H-LYP level. There are complexes with energies less than those of the reactants or products located at the entrance or exit channels, which indicates that the reactions may proceed via an indirect mechanism. By canonical variational transition-state theory (CVT) the rate constants are calculated incorporating the small-curvature tunneling (SCT) correction in the temperature range of 220-2000 K. The agreement of the rate constants with available experimental values for two reactions is good in the measured temperature range. The calculated results show that alpha-hydrogen abstraction channel is the major reaction pathway in the lower temperature for two reactions, while the contribution of beta-hydrogen abstraction will increase with the increase in temperature.